Costco takes all American Express cards, regardless of the affiliation, i.e. Costo, Starwood, Delta, etc.

Some debit cards offer airline miles as well and can be used at Costco. My friend recently showed me is Bank of America Alaska Airlines debit card. Other banks that offer airline debit cards are Citibank/AA, Chase/CO, and US Bank/NW. I haven't heard of one for UA yet. I'm sure others will hop on the bandwagon soon enough.