It would depend. If he was a guy like my ex and didn't pay child support when he did have a job (and I wouldn't be with him under those circumstances, but assuming those are the circumstances), no I would not. If he's not living up to his responsibilities on his own, I'm NOT taking over for him. He's an adult, he needs to do it himself.
If, however, he pays his child support when he has a job, and is actively seeking other work, then yes, I suppose I would help him out by paying it until he found a new job, so that he wouldn't get behind and the kids wouldn't suffer. But, I will also say that if it came down to a choice between feeding my own kids and paying his child support...his kids have a mother, my kids only have me, so feeding my kids would trump his child support. Their mother would have to find a way to make do until he got another job.