the two ways i know to get it done are as follows:
using a dye like rit brand. you fill a bucket with warm water and put in the dye. mix it up real good then submerse what your dying into the mixture. the longer you leave it in, the darker and closer to the dye color it will be. i personally haven't tried this, but there was a guy who did this to a flight stick and posted his results on the board here. fyi- i could have some steps wrong. also the color the object is will effect the the final color(yellow object, blue dye=green object...), although white shouldn't do this. you should be able to find this at wal-mart in the fabric/craft area and it's cheap.
you can also use vinyl dye which comes in a spray can. i used this method to make my cd rom and floppy drive match my cab, it came out pretty nice. i don't think you could tell they were not originally black if i didn't tell ya. this is a tough tecnique to master but follow closely and you'll have a chance...... 1. point spray can at object. 2. push button on the can. 3. wait for it to dry. heh heh. use thin layers and with 3 or 4 coats and it will look good. i found the product i used at pep boys, i think it was 5 bucks a can. they had lots of different colors.
i'm not sure how well the color will hold on a button. the dye is very thin does actually soak into the plastic(whereas paint coats it) which really helps with color fastness, but with the amount of use a button recieves. it still might fade/rub off. i have no idea which method would prove more rugged either. maybe someone else has some other ideas.
good luck.