Form 1065 Schedule L Balance Sheets Per Books - Do I enter my credit card balance at beginning and end of year?

Yes. The balance on a business credit card, just like any other extension of credit, would be included as a liability on Schedule L (Form 1065).

My Scheduke L is "out of balance" because I have no "assests". My small business only had expenses the first year and did not sell anything. Can my Schedule L be out of balance due to the credit card liability and still be correct? Or do I need to balance the Schedule L before I submit?

Are you not maintaining a separate checking account for the business. Usually, "cash in bank," inventory, and equipment you purchased to make goods or perform services will be the assets that balance your liabilities and equity.