Is there a way to store drywall vertically on its side?
You could build a drywall storage rack.


Start by building 2 or 3 triangular frames out of scrap 2x4s.





Space them out to the desired length.





To prevent sheets from sagging between supports, lay a sheet of plywood on the rack before placing drywall on it.




A rack like this may be overkill for a short term storage solution, but could come in handy if you find yourself storing drywall for extended periods. It's nice because you can store the drywall in less space, it keeps the drywall off the ground/floor, and it prevents the drywall from warping.