Assuming you mean a male member of the House Wessex or House Godwin, Edgar the Atheling was floating about and kinda-sorta involved in numerous schemes and revolts, some of which included the northern Earls Edwin and Morcar, and Sweyn of Denmark, so you could try to tweak those in his favour.
Elsewise, you could have William's victory be costlier and leave his position less secure, or you could have William die shortly after his victory (fighting rebels, illness, etc.). His kids will be underage and the Norman lords might squabble without a central figure, fight over the regency etc. This might give Edgar a bigger opening to exploit.
As for the Godwinsons, IIRC Harold's elder sons (Godwine, Edwin, Magnus) were of questionable legitimacy and his younger ones (Ulf, Harold) were babies, and William will likely have consolidated his rule by the time they can challenge him. Maybe if Leofwine or Gyrth survive Hastings they could flee into exile and champion either their own claim or that of a nephew, the one surviving brother, Wulfnoth, could also escape William at some point and stir up trouble. But, in all, Edgar the Atheling is the best bet.