Painting resiliant flooring, whether it is asbetos or not, is a more a function of the coating. You need to find a coating that can be used on asphalt or vinyl tile. The limitation is in the coatings, not the tile. The durability of any painted or catalyzed coating on this surface is dependent on the bond and hardness of the coating.

I would be more inclined to remove the tile, or apply a ceramic or other masonry tile over the top of the existing material if it is well adhered.

We're not at a financial point to do a large remodel. At that time, we will have to remove the tile. I am simply looking for something that will work in the meantime to cover the ugly. I suppose at worst it will only last a year or so... at which point we might be ready to remodel anyway.

I looked at putting down the press & stick tiles (a cheap fix) but they're about as ugly as what I have.