Over the years I have been part of churches where there have been specific individuals who (a) have, as far as I can judge these things, a genuine faith in Christ. (b) ought not to be left alone with children, as this puts the children at risk.
So you need the staff team and other congregational lay leaders to be vigilant, you need to lay down rules with the individual concerned, and you need to police those rules and review them regularly in a way that doesn't draw unnecessary attention to the person concerned.
You also need to live with the reality that some of the congregation members will be freaked out by this level of acceptance.
If the person has a criminal conviction, I would argue that they are best off attending the particular meeting at church where no children are regularly present (at our church, it begins at 7.45 am). This protects both the children and the person concerned.
[I posted this as a comment on Jim West's blog.]