I have a pedigree Cocker Spaniel who is not KC registered, would it be possible to find a stud dog and breed from her? Would her litter be able to be KC registered?

No, if she isn't KC registered, her puppies can't be either. And no reputable stud dog owner will allow thie dog to be used on an unregistered bitch. Has she had all her specialist tests for hereditary disease?

Guest I think you need to ask yourself why you want to risk your non-registered bitches life to produce non-registered pups. Your bitch may well be pure bred but if she is not registered who will know if she is or not, even you will not know unless you bred her yourself from registered dogs.