if you use something underneath the paint, you can loose the cork like appearance and texture, but i guess if you want to paint it then that doesnt really matter...
you can use a primer, and then a sealer after wards.

acrylic is prob best, but remember the cork is really ...man i cant think of the word...breathable? you know full of lots of tiny little holes and really absorbant, so might need a few coats.

another option is to cover it in funky fabric?

what is it you are painting?


(ive never actually done it myself though...)