If there's only one layer of shingles and the wood is good, you can lay another course over the existing roof.
I replaced my roof (non-island) with sheets of material called "Ondura" that I special orderred from Lowe's because I felt they would be easier for me to handle than regular shingles. I got the corrugated version and would not recomend it or use it again but they now have a flat sheet version which I may consider when I do my sheds.
Sheets are aprx 9x4 feet. Purchase in bulk is comparable to regular shingles. Your local Lowe's may not be an authorised dealer and/or you might find better prices at another retailer.
http://www.ondura.com/
Good luck!