I agree with all the responses regarding painting a
backdrop. You should definitely use acrylics, which
are extremely flexible and able to withstand frequent
stresses related to being rolled up for storage. With
acrylics, you may not actually have to stretch the
fabric unless it is lightweight. Simply weighing down
the edges should be adequate.
It occurred to me, however, that you could use an old
world map, which is already in a retractable holder,
for your backdrop. Most schools don't use them
anymore, and are likely collecting dust somewhere.
They are usually made of canvas or flexible coated
paper. One side could be whited out with gesso,
painted with the background scene, and comes with its
own handy storage! The other side could be similarly
painted with an alternative backdrop.