I've not listened to enough Eagles to know the difference between their early stuff or the more popular tracks that crop up on the radio sometimes, and that sort of style in general, but you might enjoy the lost dogs?
Lost Dogs - Wikipedia, the free encyclopedia
They're a kinda country/folk/rock supergroup made up of a bunch of singers/guitarists from alternative Christian bands. Their album "gift horse" is quite good, but hard to track down a physical copy. I gave it to my Dad for his birthday or Christmas back not long after it first came out and have been trying to track down a copy for myself for several years. It is on itunes though (along with their other albums).