Unfortunately it is still a legal gray area in the US to purchase overseas lottery ticket services, so you will find very few good options. The US-based credit card companies all shut down online gambling as an option, and unfortunately they include lottery ticket butler services under that umbrella of banned purchases.
It is still possible for US residents to use overseas butler services, but it requires you to be a little creative in finding a payment method that works.
So then once you've made the decision to try to get around the credit card situation, the next step is to find the best, most reliable (i.e., professional) company to deal with. Fortunately we've already done the legwork for you. Go to www.usamega.com and click on the game in the Marketplace section on the right side of the page. (USA Mega is not the lottery ticket butler service, but that's where you can find the links to it.)
The first thing I'd recommend before trying to place any orders is to establish an account there and make your deposit. It might take a while to get your payment method working, so don't bother with actually playing until you've funded your account.
When adding a payment method, if you don't see the USA listed in the available countries, then select a different country. One payment method they accept that is available to US residents is Skrill. It's kind of like a low-rent version of PayPal. So perhaps you will want to establish a Skrill account, and then fund your lottery account with Skrill. Just a thought -- they have other payment methods there too.
Once you get everything funded and working it should be fairly straight-forward to continue playing there whenever you want -- and of course you're not just stuck playing EuroJackpot.
Good luck!
