My friend (late 20s F) keeps asking me (late 20s F) to babysit her kids since moving nearby.

I've been friends with Rachel since high school and while we drifted a bit when I went to college and grad school, I still consider her a good friend. I recently reconnected with her after moving back to my home city for work. She had two kids while I was at school, one kindergartener and a toddler.
I've spent some time around her kids and they're totally normal, good kids. I don't have anything against them, but I'm just not fond of kids in general and I don't want to be responsible for them or spend time with them alone.
The problem is that since reconnecting with Rachel, she continuously asks me to watch her kids. She's recently started dating someone and she only has every other weekend kid-free, when they're with her ex. I say no every time but she's not getting the hint. She always pushes back with something like 'oh no, are you sure? They're no trouble!' and then finally relents with a 'maybe next time.'
But there's never going to be a time I'm free to babysit. I don't want to upset our friendship, but I feel like she's refusing to take the hint. I've declined more than five times now. I don't know how to say 'Hey, I'm never going to watch your kids, so stop asking' in a way that she won't take personally.
Has anyone else been in this position? Have you gotten out of it unscathed? If so I would really appreciate your advice!
TL;DR: My friend has two kids she wants me to babysit. I don't want to but she won't stop asking. Help!


Source.