When June Jones gave the college football coaching merry-go-round one of its earliest starts ever by resigning at SMU on Monday, the first two people to surface in the successor speculation were Butch Davis and Larry Coker.

In the day or two since, conjecture, as usual, has expanded quickly to include offensive coordinators Lincoln Riley of ECU and Chad Morris of Clemson, both of whom have fairly extensive Texas backgrounds.

Tom Mason, the interim Mustang coach and Jones’ former defensive coordinator, probably needs a miracle to become a strong long-term candidate. The team is 0-2 (0-0 AAC) and announced Tuesday that starting quarterback Neal Burcham is out for the season as a result of an elbow injury.

So unless ESPN studio analyst Davis and/or Texas-San Antonio coach Coker act publically and privately to remove themselves from consideration, both of the former Miami head coaches will remain prominent in the conversation.

That may be very unlikely. Jones was making $2.1 million annually and the wealthy private school probably will go to $2.5 million or more to reel in its next target.

Coker makes sense for the Dallas-based university.

Davis does not, and it’s not entirely because he might still be deemed toxic as a result of the ongoing UNC turmoil that began during his Chapel Hill stint from 2007-2010.

At 62, Davis still could have a lot of coaching mileage ahead and you have to assume he’s learned enough to steer clear of assistants like John Blake and players like Marvin Austin if another chance does come along.

But SMU would be too much of an awkward fit for Davis and the school, even though he quickly rebuilt the Hurricanes in the late 1990s after having worked the six previous seasons on the Dallas Cowboys staffs.

The fact that SMU’s program received the most severe penalty in NCAA history in 1987 and part of ’88 screams that almost anyone other Davis would be a better choice, even though Davis was never directly reprimanded by the NCAA for anything that’s unfolded then or since at Carolina.

When UNC fired Davis in July of 2011, his contract was paid in full. Then chancellor Holden Thorp and then AD Dick Baddour never placed blame for any of the dishonor on Davis’ plate.

But no degree of plausible deniability could separate Davis from the widespread misconduct that went on during his watch.

And if SMU needs any additional incentive to go in another direction, plenty of humiliated Mustang fans and alumni still remember that one-time Tar Heel assistant Bobby Collins was the SMU head coach when the NCAA first detected that payoffs were going on within the program.

Collins left Southern Miss for Southern Methodist in 1982 and won 31 of his first 35 games in the old Southwest Conference before being forced out after a 6-5 record in 1986.

As with Davis at Carolina, Collins technically was cleared of direct wrongdoing by the NCAA when the so-called “death penalty” was imposed a year later. But his reputation was damaged to the extent that he never landed another head coaching job. Collins was 53 at the time.

Coker, who followed Davis at Miami, 60-15 overall in six seasons but a 7-6 (3-5 ACC) record in 2006 led to his firing.

At UTSA, Coker has performed admirably (20-16 overall, 1-1 this season) in a challenging situation.

There’s good reason to believe either Coker or Davis would have success at SMU, which is battling for attention in one of the nation’s biggest and busiest media markets.

But Coker, if hired at season’s end, could devote all of his attention to coaching immediately. Davis would have to spend substantial time describing what happened at Carolina and why.

Of course in the ECU and Clemson fan camps, there’ll be some uneasiness all season about the futures of Riley and Morris. Eventually, both high-octane offensive engineers will get head coaching jobs. But for now, SMU seems bent on finding someone with experience as a winning head coach.