I have maybe 8or 10 lawns out of hundreds that have "some" Centipede in the existing lawn. I do not treat any Centipede lawns so to speak. My main concern is not killing what the customer has as "part" of their lawn.
I usually use a higher nitrogen lower potassium granular fertilizer at a very low rate and spot spray weeds with herbicides I know are safe for use in Centipede. Our soils are acidic here so that is generally not a big concern. With so little to treat, and in scattered patches like it is, I can't really justify a "special" program just for centipede.
It seems like(at least with what I deal with here) Centipede almost does as well with almost nothing done with/to it as it does with constant attention. That's been my experience with it anyway...
"The Poor Fish" circa 1930's: The Poor Fish wouldn't have been caught if he'd known enough to keep his fool mouth shut.