I dont know if it is the correct way to show the birds I dont want to be bit... but when they nip I lightly get ahold of their beak with my fingers, look them in the eye and say "no". They seem to get the idea pretty quick but there is a lot of risk to your fingers if they decide they dont want to be told no. I'm nowhere near an expert in this, I just go with what feels right and hope the experts here give me guidance.
That's pretty much what I do... "Knock it off." is the phrase I use for pretty much all bad behaviors. They all know that one in context...
And if we're playing, and they start getting carried away and apply too much bite pressure, then I do the same thing. Stop the game for a second and tell them "That's too hard."