My father has permanent residency and was deported, how can he come back legally?

My father (US and North Carolina resident) has had his permanent residency since the 80's and made the mistake of not applying for citizenship. He also made a mistake last year by catching a drug charge (intent to sell and distribute) that was a felony of course. He didn't get a sentence but was given probation for 5 years and finished in a year for good behavior I guess you could say. After he paid his dues, he renewed his residency and received it with no issue. Weeks after that, he was unexpectedly taken by immigration and is now waiting to be deported (Immigration says there's no chance of him getting out of it). What does he need to do to get back. My mom (US born citizen) is moving to Mexico with him after he's deported. What steps should be taken? Please help.