Posting can be quite tricky to learn, and very difficult to perfect.
I also agree with using a crop, just try not to get too reliant on it. Just use it until your leg muscles are strong enough to cope with the movement of posting as well as apply enough pressure to keep the horse moving. Being able to use a crop is a good skill but having nice, consistent leg muscles is much better!
If your instructor won't let you use a crop, simply apply pressure everytime you sit. Rise, sit and pressure, rise, sit and pressure, rise, sit and pressure, until the horse either decides it's enough and keeps a consistent speed or until the end of your trotting session- whichever happens first. If this is making you too wobbly try applying pressure only once in a while and see if that keeps the horse trotting.