Depending on the size of the shed roof, I think that a white cool-roof coating like Henry's HE687 would do the trick.
It will reflect a large amount of the passive heating that makes sheds so uncomfortable in the summer and will protect the roofing and the materials inside the building. This coating is easily rolled on with a thick-nap roller. It is specified for roll roofing, but should be able to be used with the shingles that you have.
You can also apply a roll roofing, but it will look like hell. Replacing the shingles is cheap, and once you have done it, it is technically easy. All the manufacturers have directions on the inside of the packaging to help you figure it out. It is dangerous work as you can fall off the roof, but you can get a new roof for about $150 per 100 sq. ft. (also called a square) if you do your own work.