Hi jchesnes1,
Many years ago I worked for a guy who was determined to jazz up a dropped ceiling by painting a select few tiles bright colors.We did it with latex semi-gloss, but in hind sight, flat or eggshell would have been a better choice.
If you're looking to "recoat" stained tiles there are ceiling tile spray paints available or stain kill will work.

Sounds like Matches is saying you should remove the tiles and paint them individually. And I suppose you could paint the cross supports while the tiles are removed if you wanted to. Sometimes they get rusty and bad looking. It would also give you the option to use a different color for the grid from the tiles -- could be a nice effect.
It probably wouldn't be practical to try to roll or brush the tiles while they're in place.

Remove the tiles, spray them with either a spray paint or (better) a paint sprayer-gun with paint designed for ceiling tiles, and paint the metal when the tiles are off.

Rolling or brushing paint on dropped-ceiling tiles generally will not get the paint into the creavices and holes, and the old color will show through those holes.