There are no credit cards that you can apply for with a co-signer.  All credit card offers, terms and interest rates are based on the credit history of the individual.  Credit cards are not like auto loans or home loans, in which co-signers are allowed.  If you are unable to get an unsecured line of credit without a cosigner, you should apply for a secured credit card where a security deposit serves as collateral against your loan in the place of a co-signer.
On the other hand, if by co-signer you mean authorized user, then yes, this is something that you can do with a credit card.  An authorized user on a credit card is someone who has access to usage on the account, but is not responsible for the bill.  The primary account holder is fully responsible for the bill. However, the activity on the card will show up on the authorized user’s credit report.