If you don't want to book a private tour, you could try going your 1st/2nd day in Rome, as early as possible, and see if you can book one at the ticket office. When we were there in early Sept, 2014, I was prepared not to do the underground. I didn't book ahead. My mom and I walked over as soon as they opened (our apt was only a few hundred meters away, so we didn't have to rely on the metro - a two min walk and we were there) and were able to get a slot for that afternoon, just after lunch. Perhaps they had cancellations. Perhaps they leave some spots for people who just show up. I don't know. Perhaps we were just really lucky, but I'm sure we had a few options for that day.
If you have more than a few days in Rome, I'd suggest going early (to avoid waiting in line for an hour + only to be disappointed) and see if they have anything avail over the next few days. Hope you have some luck. I tried asking at the Palantine hill ticket booth first, but were directed to go to the Col ticket booth.