You should use an electronic current limiter, else you will lose too much voltage in normal operation.
For instance, to limit the current at 125mA you need 9/0.125=72 ohm.
But if the load normally draws 100mA, then you lose 0.1*72=7.2V, leaving you with 1.8V to do the job.
Resistors are never good when you have to limit the current to a level close to the normal operating point.
An electronic fuse may be the mystical solution you asked for, but also a Polyswitch PTC fuse may work. It depends on your specification for normal operation and maximum tolerated short circuit current, both yet unknown.