Opener David Warner broke a thumb during Saturday's second ODI and was replaced by Yorkshire's Aaron Finch.
Injuries to all-rounder Shane Watson (calf) and Coulter-Nile (hamstring) in that game have forced the tourists to raid county cricket again.
John Hastings and Peter Handscomb join the squad for Tuesday's third ODI.
Seamer Hastings, 29, has been Durham's overseas player this summer. He has played 11 ODIs for Australia, with his last international appearance being his only Test in December 2012.
Uncapped wicketkeeper-batsman Handscomb, 24, born in Melbourne to English parents, has been playing for Gloucestershire this season on a UK passport.
Although he has featured for Australia A, if he were to appear for the full international side, it would threaten his ability to continue as a "domestic" player in England.
