Yes you can find paint that will stick to formica cabinets. That's the least of your problems though. The biggest job is to prepare the formica cabinets. Then you'll prime them and apply two coats of paint. In the end you'll have a nice looking kitchen.

We recommend that you use one coat of Zinsser's latex-based Bulls Eye 1-2-3 Primer-Sealer and then apply two coats of Benjamin Moore® Kitchen & Bath 100% Acrylic Latex Satin Finish N322.

Benjamin Moore claims that the paint is self priming, but in the case of your cabinets, we recommend that you prime them. The paint comes in a variety of colors and is a latex paint that is especially designed for ares that get water and moisture. It also has low VOCs. See our article for some suggested kitchen paint colors.

Just how well the paint will adhere will depend on how well you prepare the cabinets:

1) Take off the cabinet doors and place the hardware (hinges and pulls/knobs in a solution of 404 cleaner. This usually cleans them up pretty good. Use an old tooth brush if they are in bad shape.
2) Wash the cabinet doors and frames with a 50/50 solution of household ammonia and water to remove cooking splatter from cabinets. Works equally well on walls. Do this twice if the cabinets are in bad shape. (Note you don't have to point the inside of the cabinet doors).
3) Lightly sand the cabinet doors and frames with 120 grit sand paper. Remember you only want to rough them up so that the primer will adhere to the surface. Either do this by hand or rent a small hand sander.It is messy so either close the door to the kitchen or hand some plastic sheeting. Buy a mask so you don't inhale all the dust.
4) Clean off the sanding with a damp cloth or tack cloth. Tape the wooden trim
5) Use Foam rollers and apply one coat of the primer. We usually give it 24 hours to completely dry.
6) User Foam roller and apply one coat of paint. After 8 hours apply the second coat.See label on paint can.

Send us a picture when you are done and describe how it went.