Can I paint a tin roof without a big expense and it last a reasonable amount of time? And what kinds of paint are best for this?
Where do you live? I lived for a short while in Virginia, where metal roofs are common. There you can find firms which specialize in metal roof maintenance and painting in the phone book. I don't know what they paint with, but they produce some strikingly attractive colors and combinations which seem to last for many years.
In northern and midwest states, where asphalt shingles are the standard, roofers don't seem to know what to do with metal roofs. They usually brush on some aluminized mobile home roof coating, which I guess is OK.
I notice that a web search for "roof paint" turns up quite a few hits. If it were my roof, that's where I'd probably start.
This company has pretty good stuff for walls and Roofs seems their specialty
& will ship 5 gal pails & their people will actually talk to you and make good knowledgeable recomendations.
They have the standard paints and high reflective - high emmittance coatings.
Here is a link that might be useful: http://www.natcoat.net/
I bet you don't have a tin roof. It's probably aluminum or galvanized iron based sheet metal (Low Carbon Steel). Aluminum will not need painting. The life of the sheet metal roofing can be extended with finishes compatible with its coating.
Try posting the question on the Paint Forum here.