I pay child support for a 22 year old student and an 18 year old student who just refuses to see me! Would I be eligible to drop or possibly reduce support?

Probably not. Support is rarely tied to visitation.

On the other hand, at their ages support shouldn't last much longer.

I think you need to deal with the issues of why they don't want to see you, not try to blackmail them into it.

I pay child support for a 22 year old student and an 18 year old student who just refuses to see me! Would I be eligible to drop or possibly reduce support?

No, visitation and support are not connected, Many fathers never see their children but will still have to pay.

You need to review the child support orders to see how long you have to pay, since the oldest should be getting close to the end of most support orders.