I am installing sliding closet doors in a non-standard space. The space is wide enough for the doors but 2-4 inches too high.

In the opening there are studs on either side but on top there is only drywall. I thought I would install a 2x4 in the opening and hang closed doors from it, but how can I best install the piece of wood, given there are no studs from which to hang it? Any suggestions or is there a better way?