You'll have no trouble getting a taxi at the airport to take four people (technically, no taxi is suppose to refuse four, but some do).

As for the credit cards, you may have to wait through an available taxi or two, since not all taxis take credit cards, but you will be able to find one that does.

If there is a taxi-line manager pointing people to cabs, just tell them you need one for four people that takes credit cards, and they'll sort it out.