I would not let your baby 'cry it out'. Babies cry for a reason and we should respond to that especially at 2 months old! Sometimes when new little ones do this it's because of something else. Is he having stomach problems, like gas, etc. That can be painful and make it hard to nap. If you are nursing, cut out the cow's milk. If he is on formula...cow's milk formula, then that would be the culprit as well.
Another thing to think about is what position he sleeps in. My children (I'm pregnant with my 5th) liked sleeping on their sides and not their backs. I got those wedges to keep them on their side. Then, when I felt they were okay, I let them sleep on their tummies....they really slept good then.
Another thing that happened with my children, is my boys slept fine with naps and nighttime in their bed, while my girl did NOT. She just wouldn't sleep in the crib. But, she slept great in our bed. That was the only way that she would actually get some sleep. She needed that extra bonding/cuddling to get herself to sleep. Sometimes I would actually lay down beside her and then once she was about asleep or asleep (since you are a first time mom, you can get the sleep too), I would leave. It worked every time!
Well, good luck with your precious little one!