The Scholars League would be a consortium of five 4-team divisions consisting exclusively of Division 1 FBS schools that are either privately funded or a U.S. service academy... essentially branded as the scholarship version of the Ivy League...
And only a little more seriously... this would make for a somewhat intriguing bowl game every year, ie, to take the two highest-ranked private schools not participating in a BCS game and call it something like the Scholars Bowl... eh?