Can you sue someone for promised registration papers for a dog you purchased?

Realistically, you can sue people for almost anything. Whether you can support your case and win the suit is another issue. If provision of registration papers was part of the negotiated purchase and you did not get them then the seller is in violation of said contract; the buyer would have grounds to file suit to recover the missing product and/or financial compensation in court. Consider filing in small claims court if the seller is not willing to complete the transaction as agreed. Additionally, you may have buyer's protection if you used a credit card to pay for the transaction; contact your company to inquire.