Well, you posted in the Electric Motors and Motor Controls forum, so I ASSumed that it had a motor on it! :-/
Many vibrating feeders use a small electric motor with an eccentric weight as the method of generating vibration. If your's doesn't, then you will need to determine how it is creating the vibration. Some do it with a PWM type DC controller, others with an AC solenoid type device. IF you have a little PC board or a "black box" that your 120VAC goes into, it is most likely a PWM style controller. Many of those have a ramping function built-in, are you sure your's doesn't? If it is electronic and it doesn't have a ramp function already, varying the voltage may not work. The electronic controller would likely just shut down.
If you have the solenoid type, you will have the AC wires going directly to what looks like a short plunger assemly, where the plunger vibrates up and down or back and forth. With that type, you may be able to ramp it by simple ramping voltage. In that case a small motorized pot like what sried mentioned would be the simplest method. Another alternative would be an SCR phase-angle voltage controller. Phasetronics makes a low cost unit called the EP-1 that would cost you around $140, but you would need to ask them to modify the ramp time to be 180 seconds instead of 60 seconds. They will do it for you if you ask nicely, it will just take longer to get it.
"Venditori de oleum-vipera non vigere excordis populi"