I've only played this a few times with my band, (and I can't remember how much we covered the Eagles, or if we just played the song). But I've strummed it:

D - D - U - U - D U (repeat)

Bluesman Jack's right though, it's more a feel than actual strokes. Try playing along to the record - this should help you get the chord changes exactly right - once you know were you're starting and supposed to finish, a lot of the time the rhythm sort's itself out (with practice and patience of course.)