The ability to control a single phase motor with a VFD is prone to stall at the lower speeds, the only type that I know of has been Capacitor-run motors, Motor that are capacitor start only, suffer from the problem above.
IOW I would put a three phase motor on if you really want Variable speed drive.
In any case, you may have to search a bit to find a VFD that even attempts to run a 1ph motor.
Al.