Well, it's a bit nasty, but if the belt's run is long enough, and there's enough room for an idler to replace the motor's pulley (in a similar position), arrange for the belt to be driven from the middle of a long run, with the motor's axis at 90 degrees to the plane of the belt. To do this, the belt has to be twisted 90 degrees. Twist it one way, and drive it from the appropriate side, and it'll go one way; twist it the other way, so you can drive it from t'other side, and it will go in the opposite direction. You'd need to arrange suitable idlers to get enough belt wrap. Of course, this means arranging for the motor's axis to be rotated 90 degrees, so it's pointing at the side of the (untwisted) belt, ie at 90 degrees to the driven pulley's axis. Hope this is clear…
Otherwise, arrange idlers to provide a lot of belt wrap, and drive the belt from its 'outside', as if a flat belt.
Resorting to gears is probably not such a bad idea…