Is this the best way to conjugate "cheerlead"?
they cheerleaded for it just the same
"Cheerlead" becomes unrecognizable when you say "they cheerled", so I'm guessing this is why you don't conjugate it like "lead", but I cannot find any references that include conjugation of the verb. This is not the same issue as found here, since it's not about the placement of the suffix, but rather the choice of suffix.
EDIT: I think @KristinaLopez is correct, if you're speaking about literal cheerleaders, although the context here is more figurative, casting the media as "cheerleaders". If you say the media "cheered", it doesn't have the same connotation of "leading the cheering for". I suppose though "cheered" still is correct in that case, and you'd need to recast the sentence to get the word "cheerleader" into it, such as:
..., and yet they acted as cheerleaders for it just the same