If the screws really are stainless steel then you don't want to paint them at all. But you may need to clean them.
If they are plain steel then there are many two coat and three coat system that have proven to have very long life.
Thanks for your help. I've decided to use A4 stainless steel screws, possible with a black oxide finish. I've chosen A4 (316) stainless steel because it is more corrosion resistant than other types of stainless steel. I know that the black oxide coating won't provide corrosion resistance, its just for aesthetics. The screws won't be cleaned because the coating will wipe off after a while and turn the screws silver again. So I'm going to look for some thick wax to put over the top of the screws. Do you happen to know roughly how often the wax should be applied? Please could you tell me if you think its more like every 3 months, or every 3 weeks?
What is the exposure? Lots of sun and very hot? Lots of rain?
The more abuse the more often.
Just be advised that if your wax serves to trap moisture under the heads of the screws then you may be accelerating crevice corrosion and/or galvanic corrosion.
But why cost them?
Generally, stainless steel (such as SS 316) has own corrosion resistance against atmosphere, except for marine environment or insulated pipe. Actually, the definition of stainless steel is the steel which is having more than 11.5% Cr (SS 316 --> 18% Cr) and it is to form own protective oxide film(ex., Cr2O3) on the surface and does not require any coating at all against atmospheric corrosion, generally.