The definitive guide to badges and many other aspects of the original '60s Cobras is Rinsey Mills' 'Original AC Ace and Cobra', published by Bay View Books, ISBN 1 870979 14 1
Original AC Ace and Cobra | eBay
Very expensive and out of print, so here's a summary of badges on the 60s cars:
Mk1 and II
Up to chassis CSX 2054 - 'Shelby AC Cobra' motifs front and rear
CSX 2055 to CSX 2132 - the 'flat headed' Cobra emblem front and rear
CSX 2132 onwards - the later Cobra emblem front and rear
Early COB/COX chassis cars (sold outside US) - 'flat headed' Cobra emblem on front, AC badge on rear.
Later COB/COX chassis cars - later Cobra emblem on front, AC badge on rear.
Mk III
CSX chassis cars - later Cobra emblem front and rear
COB/COX chassis cars (with 289 engine) - AC badges front and rear.