Can a person who has a permanent ban be allowed in the u.s. on a tourist or work visa?

There is a nonimmigrant visa waiver under Section 212(d)(3) of the Immigration and Nationality Act. It waives most of the grounds of inadmissibility, including aggravated felonies. He may apply for this waiver in conjunction with an application for a tourist or working visa. The waiver request needs to be recommended by the U.S. Department of State and approved by the U.S. Department of Homeland Security. They will look at his record, the nature and recency of his conviction, his eligibility for the underlying nonimmigrant visa, his reason for wanting to come to the U.S., whether his admission would cause any risk, and whether his admission is in the interests of the United States. This is something he may want to consider doing in consultation with an immigration attorney that has experience with this kind of case.