From what I can recall, watercolour being toxic... no. I'll do some research into that though first. Just for now, don't paint near your birds until we find a definite answer.
Basically, all the information I've come across so far is saying that 'water based paints' (water colours and others that are waterbased) are fine, but - for double safety, I'd advise another room, with the window open.
Oh, and don't use solvent cleaners for your brushes and such!
I am very careful when having anything with any fumes near cooper. but water based paint shouldn't do much, but your bird might be uncomfortable/. I would move him/her as far away as possible with a window open.