Cobbs has been a regular presence on TV since the late 1970s. After snaring a small role in "King" (NBC, 1978) he went on to the "NBC Live Theater" presentation of "The Member of the Wedding" (1982) and "Rage of Angels" (NBC, 1983). Cobbs worked with Black theater legends Ossie Davis and Ruby Dee on their PBS anthology series, "Ossie and Ruby", starring opposite Dee in "My Man Bovanne" (1987) directed by Davis. He was a regular on the short-lived ABC sitcoms "The 'Slap' Maxwell Story" (1988) and "Homeroom" (1989) and did guest shots on numerous series including "Designing Women" and "LA Law". Cobbs may be best remembered for his portrayal of Lewis Coleman, the strong traditional father of Regina Taylor's character on the acclaimed dramatic series "I'll Fly Away" (NBC, 1991-93) a role he reprised for the PBS TV-movie conclusion "I'll Fly Away: Then and Now" (1993).
Cobbs has also appeared in over 20 features since the late 70s including "The Brother From Another Planet", "The Cotton Club" (both 1984), "The Color of Money" (1986), "Bird" (1988) and "New Jack City" (1991). More recently he played Whitney Houston's manager in "The Bodyguard" (1992) and an old partner of defrosted anachronistic cop Sly Sly Stallone in "Demolition Man" (1993).