Pre-arrange is probably easiest for you. I would use a local travel agent that is contactable in advance to make your Manohara hotel reservation and the car that will pick you up at JOG and deliver you there, with intermediate stop at Prambanan. You can do this on the fly, but it eats up precious time finding a willing car for a good price, and in the end, I don't think will save you all that much cash. Your time is the most valuable commodity you have on this quick stopover. Do a search on other threads and other forums, but try emailing the following:
www.travelindo.com
I used them a few years ago for some reservations with good service and results.