Even a plain green Amex would be fine. Call Amex, explain the situation and if you already have your own Amex, ask them to transfer the miles to that card. Amex miles do not expire and can be transfered within 1 minute to any airline you want, when you are booking award tickets. If you transfer the miles to an airline program, they will all expire after 2-3 years, if you do not travel with that airline during that time so the clock would be reset, plus you do not gain status because they are not MQM miles.

Domestic travel for 2< child is free in the USA, anything internationally is 10% of the current purchase price of an adult ticket, and has to be in the same class fare as the parent's award ticket. The best programs with domestic and multiple international partners/connections are Delta and United/Continental. If you travel a lot in the USA, DL has the best connections/rerouting; if you travel internationally then take UA, (I mean connections in general, not just award ticketing, because you would have to continue flying with the same carrier to reset the clock for the miles).