Well ... you probably could ... but why would you want to?
Are you keeping your birds indoors as household pets? Or do they live in an outdoor aviary? The link below has a wealth of lorikeet behavioural info .......
Rainbow lorikeets can become highly aggressive when their hormones are raging and I imagine providing them with a nest box would only serve to over-stimulate undesirable behaviours. If you intend to keep them as household pets, I would not recommend any kind of nesting materials in an indoor domestic situation.
I have 2 male Cockatiels that are bonded to each other.
I give them a box with doors cut into it and they play in it a lot.
I have no idea how 2 male Lorikeets would get along.