A potential customer presented us with a US Department of Homeland Security, U.S Citezenship and Immigration Services Employment Authorization Card.. I am not familar with this card. It does't say that it is and identification card, would you use this as a valid form of ID for CIP?

The best place to see exactly how it applies to your institution, based on your risk assessment and documented procedures for verifying an individual is to reveiw pages 45-48 in the FFIEC's BSA/AML Manual. It outlines very clearly what is expected if the customer is a US person vs. a non-US person, what you need for documentary verification, etc.

Form I-766 is not issued as a form of identification. At best, it could be considered as secondary identification if presented in conjunction with a foreign passport.

If it is not listed in your CIP as an acceptable form of identification, then it simply is not.