I don't know if there is a newspaper for Avondale. However, if you're looking for obituaries, contact the Opheim Community Library in Valley Co. Call them at 406-762-3213.
Contact the Poneer Museum of Valley County, www.valleycountymuseum.com/Home.html
who has "an extensive genealogical archives and Western Reading Room. . ."
Successful Searching & Happy Holidays!