It makes tons more sense to me for the DK in DKC to be the grandson of the original one. For one thing, Cranky is so old. If he's just DK's dad, you would probably expect DK to be around 30 at the very least (that's going by human years, but they're cartoon characters, not real apes). I'm pretty sure DK is younger than that.
Also, in DKC, the first Rare DK game, Cranky is supposed to be DK's grandpa, and in DKC2 Cranky (apparently mistakenly) calls himself Diddy's grandpa. Though the latter thing is most likely a mistake, it seems to indicate that DK is Cranky's grandson because DK and Diddy seem to be from the same generation (correct me if I'm wrong about that).
Don't get me wrong, it's not that I have a bias against DK64 (which I think is the only game where Cranky refers to DK as his son); it's my favorite game in the series! But I have to take one of the positions due to Rare's inconsistency, and I happen to think that the grandson theory is the more likely one (and I also can't really picture the annoying little DK Jr. in GBDK (DK '94) as the Donkey Kong of DKC.