One way to put a painting on clay is to paint it on paper and transfer the result onto your clay piece. Some people are real masters of this method, transferring several layers and what have you on the same piece. All you need is newsprint paper and underglaze colors.
I decided to take art therapy approach and painted 4 giant bugs. Yes, I suffer from entomophobia, fear of insects, bugs are the worst, especially flying ones.
Once your image is ready it has probably dried out but that doesn't matter. You can give it a quick mist of water with a spray bottle and place it on your leather hard clay piece. Make the reverse side VERY wet with a brush or sponge. Leave it in place for a good while and rub it in with a soft rib to ensure good transfer. You can lift the paper a bit to see how well your image is transferring. The parts that aren't sticking to clay need more water and rubbing.
I transferred my bugs on a milk carton which was actually already bone dry... but it worked quite fine anyway. Now I'm just praying that this isolation will end soon so that I can get my bugs FIRED!