My husbands kids want to come live with us but he is a registered sex offender. The charge has nothing to do with children and he's wondering if there is any hope he will get custody

Normally, depending on their ages, and also on which state you are in, the children's' preferences might be considered but are not dispositive. In most places, assuming the custodial parent fights it, you husband would have to prove a material change in circumstances since the time of the original custody decision. And obviously, if the mother does fight this, she will probably try to use his prior conviction (for whatever it is for which he is a registered sex offender) against him. Whether the judge finds that to be relevant is up to the court.

he's wondering if there is any hope he will get custody

There is always hope, but no one can predict what a court will do, especially with so little info. As noted, there are lots of factors that would be involved in a judge deciding to modify the original custody order. If you want to give us more background we may be able to advise better on the chances.

In the meantime, if you want to pursue this hire a very good Family Law attorney in your area.

Have you and your husband talked to any attorneys in the area? That would be a good place to start. I'm not going to ask what his conviction was for but there is a very good chance it will come up in court. Are you asking if there is hope because he doesn't want to try it if there isn't a great deal of possibility that he can gain custody? Basically I ask that because we can not predict what the judge will decide there are lots of factors that go into making that decision. Some of them have already been addressed above. So unless you want to give more details on here my best advice right now is to start looking at attorneys.