Jack Johnson fought Joe Jeanette 7 times. There have probably been a rivalries which contained more battles, but that one crossed my mind first.
It must be either Langford v wills or Lewis v Britton. We're talking double figures for fight numbers in them cases.
Might be Langford/McVey. I am willing to suggest the answer (amongst established fighters) probably involves two from Langford, McVey, Jeanette, Clark or Wills.
Jack Britton fought Ted Lewis 20 times Othe rivalries with lots of fights include: Sam Langford vs Joe Jeanette 13 times Sam Langford vs Sam McVey 13 times Sam Langford vs Harry Wills 18 times
Sandy Saddler fought Willie Pep four times. Chacon fought Limon 4 times. Vazquez fought Marquez four times. Baby Arizmendi fought Henry Armstrong 5 times. Sugar Ray Robinson fought Jake LaMotta six times. Langford fought Jeanette 15 times and Wills 22 times.