They should definitely have an ability that has something to do with turning things to stone, because that's what makes a cockatrice a cockatrice.
Maybe something somehow related to earth creatures, quanta, or marks? Something like
= infect, maybe? That might make it too good, though, but cockatrice needs something, at least in the upped version, because in upped play, it's basically giant frog 7-12. In unupped play, at least there's more of a difference, with +1 attack/def for +1 cost, but in upped it's +2 def for +1 cost, and that's not really worth it.