FWIW, the tourist booklets in Bali do advertise day tours to Borobudur and Prambanan. If one takes the early flight from DPS to JOG and an evening flight back, it appears to be more than enough time if one wants a fleeting glance at both sites.

We got out of the airport around 10a and got to Prambanan about 15 minutes later (it is very close). Spent over 2 hours there (you can do a quick visit in 30 minutes). About 1 1/2 hrs to Borobodur from there. Many visitors may only spend 1 hr here. Our stay at Manohara (some of the older rooms are being renovated and are very nice though a bit small) let us in the back so we had all afternoon to spend onsite, as well as a good part of the next day (paid for the sunrise admission).

We booked the Manohara through travelindo who provided a lower price than direct though one had to send them addvance payment through paypal.

Car was arranged through jogjarentcar.com