Helpful information to a very limited number of readers (but it helped me).
The library system here in Amarillo, Texas does not offer ebooks; however the Lubbock public library (a city about 120 miles away) offered library cards to any Texas resident (not only city or county residents),
http://library.ci.lubbock.tx.us/libCard.aspx . The Lubbock library is even offered ePub books! So during my next trip through Lubbock, I stopped off and got my library card and now I'm set for ebook rentals.
So my suggestion is to check the web sites of nearby cities to see if there are nearby options that might be of use to you.