Not that I rely on Geni, but they have some interesting data to review.
I'd say at the very least we could use some of this to do some fact checking on them. I've found many times they're right, but just need some sourcing to back them up - however, I've also seen blatant errors there too - so use with caution.
Geni shows a second wife, Elizabeth, 2 children, and a sibling.
And here's another link, that may explain why Geni got it wrong...
According to the article, there was more than one Thomas Paine around at the time, and they often get confused together. So yet another caution to watch carefully to keep them separated.
One more link. Bio states that "Paine's wife and child died in childbirth", so he may have had a child with Mary, but the baby was born and died on the same day (according to them).
So I don't think he had any children, but we might conceivably connect him through parents or wife.