We are considering introducing a new checking account product geared towards customers who may have had issues in the past perhaps with chexsystems and etc; are there any regulatory requirements that would not allow for restriction of debit card capabilites?

You could establish lower daily cash and spending limits for cards attached to such accounts. You'd have to disclose those tighter restrictions to the customers, but I don't see a regulatory problem. Are there any particular types of limits you're thinking about?

We are considering not offering a debit card to these customers.

Dsalarey - there is no Federal regulation preventing you from not offering debit cards on these accounts. You might want to verify with your state laws, though.