You can't, we are sorry. As most online services we charge up front. That makes for lower administration costs. Easier for us and we can keep our prices low for you. You can pay by credit card, PayPal and a few other payment methods depending on your location.
You will still get an invoice for every payment made. You can find them on http://twittercounter.com/pages/pricing.
On this page you can also find all your payment details and edit them.