My son has 2 felony convictions and is serving time for his second now. I am his mom and I am starting a business. Question is; Can he join me as a partner in my business when he gets out? Is there a law saying he can't?

It depends on the nature of the business! You can describe it here if you want.
His PO will know anyway, so you can also wait until then.
(PS: 'convicted felon' can be just felon. All felons are convicted felons.)

In a private business maybe. Depends on the felony charge. If it is about money, may not be able to get bonded if necessary. And yes, never met an "unconvicted" felon.