Where did you get this phrase?? I love it. Give us some more context please but i do think Teacher Jan has got it covered.

Do you mean tummy time? https://www.webmd.com/parenting/baby/features/tummy-time#1

You REALLY needed to include context for this. REALLY. Next time you ask a question about a tv episode, include the dialogue before and after. That said, I was able to look it up. "belly time" is not a common phrase. In this situation, Susan has spent some time talking to Ross & Carol's unborn baby by speaking to Carol's stomach (or Carol's "belly"). Ross is saying that he thinks he should also get to talk to the unborn baby, too. Another way of saying that would be that he should be able to spend some time talking to Carol's belly or he should get some "belly time." There's no way to guess what that sentence is about without knowing the episode or the context. Include the surrounding dialogue next time.

Tummy Time is one of baby’s first exercises—and the most important! Tummy Time is the period during the day your baby spends awake and on their stomach. It is a crucial exercise for baby’s visual, motor, and sensory development. Baby can begin Tummy Time as a newborn, and continue throughout baby’s first year