How to purchase Lion OS without going to Mac App Store?
Just to note, you can (at least in the UK) use the App Store with a debit card.

However, if you don't have one of those either, and you're not having any issues with OSX 10.6, why not continue using it for now? In August, Apple will start selling 10.7 on a USB drive, which you can purchase with cash in an Apple Store.