You know who doesn't have two? OU.
Missouri probably doesn't have two genuine rivalries either, which is probably why many of these prognostications show OU-Mizzou as one of the "permanents."
OU of course played Missouri for a long time--96 games (67-24-5), starting in 1902. But Missouri's biggest rivals were (1) Kansas and (2) Kansas State. And OU's biggest rivals were (1) Texas and (1a) Nebraska. OU fans didn't like going to games in Columbia, because they thought that Missouri fans were jackasses. But that didn't make the "rivalry" anything special.
OU and Arkansas have played 15 games (10-4-1), but only 3 times since 1926. And Arkansas has a longstanding rivalry with/hatred of Texas. I think Arkansas will be one of Texas' permanent rivals, but not one of OU's.
OU and Texas A&M have played 31 times (19-12), and I think that a lot of OU fans would like to see the Aggies on the schedule. But I don't think that OU would be A&M's preference and I doubt that the SEC will make OU-ATM a permanent.
Other OU vs. SEC series:
Alabama 6
Auburn 2
Florida 2
Georgia 1
Kentucky 3
LSU 3
Ole Miss 1
Mississippi State 0
South Carolina 0
Tennessee 4
Vanderbilt 3
So, obviously, OU-Bama should be a permanent.