Typically "charges" means that it's a criminal offense, and if so, you absolutely should not go with an online service. Get the best lawyer you can afford, and deal with the inconvenience of phone calls. Especially if you're facing jail time, do you really want to run the risk of being inadequately represented?

If it's a civil suit, you should still should weigh whether the inconvenience of phone calls is worth risking a judgment against you.

As for credit cards, some (perhaps most) attorneys accept credit cards, and my assumption is that nearly every online service will accept them.

Update: You commented elsewhere that it's a traffic offense. Assuming that you're not facing jail time, this might be a case where you can do most of your communication with a lawyer by email and still feel reasonably assured that you're being adequately represented. But you may still need to make an initial phone call. Or rather, being willing to make an initial phone call will give you more (and potentially better) options.