I would like to paint the shower tray and surrounding framework. Is there a type of paint which I could use for this?

What material is the shower tray and framework?

Fiberglass

Painting fiberglass requires a Marine type paint, I believe Gelcoat is one brand you could use. Gelcoat and most other Marine paints have a mold inhibitor so it would be OK for a shower. Make sure to do all the prep work as required by the manufacturer or it will not last. Also, if you want a smooth finish it should be sprayed, rolling gor brush will leave stipple and brush marks.