Arabic written in English letters is called "Franco-Arabic". Some numbers are used for the letters that don't exist in English such as ع،غ،خ،ح. Franco-Arabic is used only on internet, so it's difficult to find a book which uses it.

There is this one: http://www.amazon.co.uk/gp/product/0615589588/ref=gno_cart_title_0?ie=UTF8&psc=1&smid=A3P5ROKL5A1OLE It is Lebanese Arabic, not sure which dialect you're looking for.

This kind of books is not available but I can help :) Tell me whwich book and I will write it for you in enlish script ^^

What kind of Arabic you learn standard Arabic or dialect so I can give you good book with English alphabet

Thanks for the effort Big Heart. What 'other' country are you from? Your English is very good.