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The only western series that ABC had in that time period (as far as I can find) was The Young Riders
. Heavy advertisements make me wonder if it was a miniseries...
I'm more inclined to think that it was on another channel. Or, quite possibly, that it was aired earlier than I was looking for. Most like the latter, because after doing some more digging, I think it is Wildside
, which seems to meet all of your criteria — except it ran in 1985 and only lasted part of a season — 6 episodes, to be precise...
TV Rage
has slightly more complete information on their page, including episode summaries and a character blurbs. Howard Rollins was your black man explosives expert, and the strongman was also an expert with a whip.

Anybody remember a Western TV show that aired on ABC in the late 80's-early 90's, I think...
The show had a father-son team who were both expert marksmen with six shooters (the six shooters were broken or modified some way. I remember the father's guns being "fixed" by the son and he couldn't shoot worth a darn anymore), a black character who was a cardshark/gambler who was also an expert with explosives, a guy that was superhumanly strong, I think a guy who was good with rope?
I can remember the theme music, I can even remember the commercials/advertisements. It was pushed rather heavily by ABC and TV Guide.
BUT I CANT REMEMBER THE NAME OF THE SHOW!