For charge card products, which it sounds like is what you're talking about, then as Centuion says you just need to pay before the next statement date. The "Pay By" date shown on your paper statement, if you get one, is really a suggest "mail by" date. The website shows the true pay by date.

You can schedule payments on the AMEX website which in my opinion is a better way to go, you can schedule it for the day before your next statement date that way.