Austria international Arnautovic has moved to the Britannia Stadium on a four-year deal on Sunday, while Ireland arrived on deadline day from Aston Villa on a season-long loan.
The former Republic of Ireland international struggled to nail down a regular spot at Villa Park, making 57 appearances over three years at the club and found himself out of Paul Lambert's plans for the new season.
Arnautovic was described as having the "attitude of a child" by Jose Mourinho during a loan spell at Inter and was also reported to have had a fight with former Werder Bremen team-mate Sokratis Papastathopoulos during training last season.
However, Coates is confident that manager Mark Hughes can mould both into quality performers for Stoke
"They are both talented players and are joining a club that will hopefully bring the best out of them," he told The Sentinel.
"Mark has been out to see the striker (Arnautovic) in Germany and likes him. He's got a bit of a chequered history on the personal side, but he is coming to a club with a squad of good professionals and that should be good for him.
"Certain clubs work for certain players and we are hoping he's going to be the striker who can score the goals for us because that has been one of our deficiencies.
"Friends of mine at Manchester City remember Ireland coming through the system there and he has since had his moments.
"His career seems to have gone in the wrong direction of late, but Mark knows the guy well and he certainly has a good pedigree as a player."
'Obviously Messi is the best player in history and being compared to him means that you're doing things right, but I try to be myself': Barcelona star responds to comparisons with Argentine legend
'Darwin Nunez would be gold for Arsenal': Liverpool legend claims Gunners should have signed Uruguayan striker in January
