Before you cover it, probably worth checking that moisture hasn't got under
the damaged felt where it could be rotting through the roof timbers (these
are usually tongue and groove and can be replaced easily if that has
I used Coroline on an old single pitch shed roof many years back and it was
pretty good, quick to use, and outlived the rest of the shed. I used an
orangy brown colour at the time and the only downside is that is a bit too
light and can look a bit scruffy when the colour wears off in places. Stick
to dark colours if you use a product of that type - black, dark green etc.
The nails for it come with colour matched plastic screw cover things so they
don't pull through. I'd suggest using foam fillers under edges though to
keep out wasps etc.
It does tend to look better on a shallower pitched roof though, so when my
small apex shed needed doing a year or so back, I opted to re- felt that
which I then coated in Thompson's roof seal.