I assume you’re talking about being a “licensed private investigator” licensed by the state to practice. In that case it can be very tricky but not impossible to achieve for a felon.
One can become an investigator for a business and not have to be a state licensed P.I… Such as being an investigator for an insurance company or working in corporate security for one employer.
Also, in many states one does not need to be licensed to be a process server. In investigations such as skip traces are a natural extension of that profession.
Bounty hunters are also a form of investigator and many states do not have specific licenses for it. But as a felon he would not be able to carry a firearm. In fact, some states do not let felons carry any weapons including pepper spray.
What was the felony, how long ago was it, and how old was he when he did it? Has he considered trying to get a pardon for it?