My now 5 month old hated tummy time too! He has a slight case of Torticollis so right around 14 weeks old we were in Physical therapy. The number one thing she instructed me to do was tummy time, tummy time. Now mind you I have a screamer and it was really hard to do with a 2yr old brother trying to tackle him all day. But I just made him fuss through it a little bit longer each day. We started with 5 minutes and now we are up to 45 minutes. As a mommy you can tell when it's just I'm not liking this fussiness to, okay I'm done Mommy get me up. I would pick him up comfort him, sometimes he needed to just be nursed, other times he was frustrated he couldn't get a toy, and sometimes he was just plain TIRED. I was so amazed how just simply working with him each day he progressed.
However, he is still having difficulties rolling over as well. And like the previous poster mentioned we've been using the same maneuver with starting the motion for him, and he still hasn't rolled from back to tummy. And just yesterday he rolled tummy to back. Granted my boy is HUGE, and the PT did tell me the larger babies, especially if they're top heavy seem to progress a little bit slower. I mentioned it to my Ped too and he said not to worry yet either, most will progress on their own timing....
Good luck and just work with the tummy time, honestly it's hard and if its your first definitely not fun too watch. My first never did any tummy time he'd roll out of it and/or scream hysterically I couldn't stand the screaming. With the second it's a little easier to handle and push him......good luck in the end as long as your little one gets some tummy to tummy time with you or even just airplane time its better than nothing...BTW when I got one of those play mats for my little guy, it made all the difference for him. Also a little extra padding at first may too the trick too!!