It doesn't matter how "tame" your bird is, or how easily you can handle them one bit when it comes to them accepting and then wearing a harness....Most birds absolutely hate all harnesses (there are exceptions I'm sure, though I've not seen one yet, lol), and just getting it on them is not the battle my friend, not at all...Once you get it on him, which you could force if you really wanted to (don't do this, I'm just trying to make a point by saying this), the problem is getting them to keep the harness on without constantly chewing on it the entire time they have it on...And i mean constantly chewing on it! Doesn't usually matter where you take them or what's going on outside, how exciting it is, etc., once they have that harness on them most birds have only one mission, and that is to get the harness off of them! And they can ignore anything and everything going on around them that you'd think would hold their attention...
The Aviator Harness is by-far the easiest one to get them to accept in my own experience, and it's also the easiest to get on them, and the safest in it's design...However, there is a really good reason that the Aviator Harness comes with that DVD/CD-ROM explaining the "harness-training" process, and if you don't follow it and just try to put it on your bird, it's not going to work, even after you manage to get it on him. So it's very important that you make this process extremely gradual, slow, and at your bird's own pace rather than your pace. And in my experience (I've currently got 3 birds who willingly wear their Aviator Harnesses without a problem, and also got my mom's CAG to accept his) this process can take from months to over a year, to never (I've got a 4 year-old Cockatiel who would sooner chew-off her own wings than keep any type of harness on, and after over a year of the same desensitization process that I've used with my other birds and then also trying other ideas, I finally gave-in and let Duff win)
Usually you really do have to start this process by "desensitizing" your bird to the harness itself. You mentioned how tame your bird is and how easily you can handle him, and I'm sure that this is true, but you have to realize that the harness is not the same as "you", and simply because you're the ones putting the harness on him does not at all mean that your bird is going to think "Oh this thing must be okay and I should like it and accept it just because they are putting it on me". That's not how this is going to work, as you've found out already. So i always start-out by laying the particular harness that is going to belong to that particular bird right next to their cage or wherever they spend a lot of time that the harness can sit in their presence and vision (each of my 3 birds has their own individual Aviator Harness that is a different color from the other's, even though my Quaker and my Green Cheek wear the same size; they need to be desensitized and accepting of their individual harness that they recognize by color, so if you have more than one bird that you want to harness-train, always get each bird their own, individual harnesses and make them all different colors from the other bird's harnesses).
So after a while of allowing the harness to sit near their cage and moving it closer and closer to the bird itself until the point where the harness is actually sitting on their cage and then inside of their cage hanging (don't put it on the bottom of the cage, you don't want them to poop on it), then I start actually playing with the bird with the harness. The idea is you want them to get to the point where they are not at all scared or at all hesitant to go near the harness, touch the harness, play with the harness, carry the harness in their mouth, etc. *The reason you do this isn't so much to get them willing to allow you to put the harness on them, but rather to get them to accept the harness once it's already on them. Getting a bird to allow you to put the harness on them has always been the easy part in my personal experience, as Wrench said, if you are only interested in getting the harness on them then you can simply start-out by using their favorite treat and then slowly put the loop over their head, and reward them, do this over and over, then put the loop over their head and then put one wing in and reward them, and do this over and over until you get the harness completely on them AND they allow you to adjust it .And this is exactly the way I train them to allow me to put the harness on them, which even with treats can take months to over a year.
HOWEVER, if you only focus on training them to allow you to put the harness on them and you don't first train them to accept the harness overall and desensitize them to having the harness near them/on them/touching them First, then what usually happens is that you'll end up with a bird who easily allows you to put the harness on them very quickly, without incident, but then once the harness is on them and it's not taken right back off, they will spend every second that the harness is on them picking at it, chewing on it, pulling on it, and depending on the species of bird they will chew right through it. And this is all totally regardless of where you take them or what they are doing once the harness is on them. Some birds do actually get distracted once they get outside of the house or in the car, or once they go inside of a store or a park, etc., where there are people and new things to see; in my experience though, that isn't usually the case.
*I actually kind of made this mistake with my Green-Cheek Conure, Bowie. I had already Aviator-Trained my Quaker and she was pretty easy, I did it the right way/the long way, and allowed her to spend ample time with the harness outside of her cage, inside of her cage, playing with the harness, etc. for a month or two, until she actually enjoyed playing with the harness and didn't care one bit that the harness was touching her, near her, etc., and THEN i started the totally separate training process of getting her to allow me to put the harness on her, one single step at a time, repetitively, with treats. But with Bowie I got a little cocky or impatient, or both, and since he was easily handled and I could touch him anywhere without a problem, I decided to just start out by training him step-by-step to allow me to put the harness on him, using treats, and this took about 2 months or so to get him to the point where I could put the Aviator Harness on him without any nipping, pulling or tugging on the harness, squawking at me, etc., and I could get the harness on him in a minute or two with no problem.
HOWEVER, once I got the harness on Bowie, that's when the problems began, as Bowie could not at all shift his focus from the fact that the harness was on him, touching him, etc., and that he couldn't get it off. Didn't matter where I took him, outside in the yard, on a walk, in the car for a ride, into a store like Petco, Lowes, Home Depot, etc., I even tried a couple of long hikes in the woods, it didn't matter. Bowie did not hardly lift his head up or remove his beak from the harness the entire time I had it on him, to the point where after a few months of thinking that he would eventually stop it and would start to enjoy just being out and about, Bowie actually chewed a good portion of the way through several spots on the Aviator Harness and I had to throw it away and order him a new one. And once I did that, I started all over again from step #1, where I should have started in the first place, and that was with getting him used to his harness being near him, inside of his cage (his safe place), getting him used to playing with it, having it within his view at all times, no matter where he was (if he was in the living room with me the harness was on the coffee table, if he was in the kitchen on his T-Stand while I was making dinner, his harness was on the counter-top, if he was in my bedroom in his sleeping cage, his harness was hanging inside of his sleeping cage and under the cover, etc.) And this continued for a good 2 months, then I went back through the steps of allowing me to put the harness back on him again, which went very quickly and he was again comfortable with this after a week or two. THEN we tried the whole thing again, and the second time around Bowie left the harness alone and was able to enjoy what was going on and participate in it. And all of these tips about desensitizing your bird to the Aviator Harness are on the DVD that comes with the harness.
**This process is definitely a marathon, it's not in any way a sprint, and it's at your bird's pace, not your pace. And it's going to require your patience, your time, etc. But if you do it the right way, the slow, gradual way, then the end result will be much, much better and come much more quickly. And it's a different process with each individual bird too, so you can't really know or even guess how long it's going to take your individual bird to get through the processes, you just have to let it flow. But once it happens you'll feel it was all worth it for sure, because you absolutely cannot take your bird outside or out and about with you without him either being on a harness or in a carrier/cage of some sort (unless the bird has some type of permanent injury or disability that makes him unable to ever fly again, like my Cockatiel, Duff has). Clipping their wings does not at all prevent them from catching a breeze/wind and taking-off, this is a mistake that many, many people have made and been forever sorry for taking a chance on. So the Aviator Harness is a great peace of mind for you, and enables your bird to go out and see the world beyond the house he lives in. So it's totally worth the effort, time, and patience.