I'm trying to book a trip on Air Asia, but I can't. I've read they don't accept American credit cards online (I live in the US). I can probably go through a third party, but then I can't pay for bags.

Recommendations?

Interesting. I booked 2 flights on Air Asia last fall on their website for flights in January, no problem. Singapore to KL & Penang to Bangkok, with a Citibank Mastercard. I suspect it may be your credit card causing the problem rather than the Air Asia site. Try a different card or call your cc to tell them it’s you booking the flights. It may help. The card I used, an AA branded card, was the same one I’d used to book flights with AA & hotels so there was no question for Citibank it was me booking. Good luck.

I too have booked Air Asia flights using U.S-based credit cards with problems. I've used both Citibank-issued Mastercards and Chase-issued Visa cards.

Could be that your CC is blocking it because of suspicion of fraud. Call your CC co. and find out. If so a release will be exercised.