Reina, 29, received a straight red card for clashing with Newcastle United defender James Perch in the Reds’ 2-0 defeat at St James’ Park.
The Liverpool number one is set to miss the FA Cup semi-final at Goodison Park and Coates believes Doni can excel in Reina’s absence.
“Alexander is a great person and a great goalkeeper. I am sure he will do really well,” Coates told Liverpool’s website.
“He has played for Brazil, one of the greatest national teams in the world, so he is used to playing in big games.
“He perhaps hasn’t had an opportunity because obviously we have Pepe, but I think he will do well.
“I think he will make the most of every opportunity that’s given to him. He is a great teammate and we all wish him well.”
The 21-year-old Uruguayan defender scored his first Reds goal since sealing a switch to Liverpool last summer with an unstoppable overhead kick in a 3-2 defeat by Queens Park Rangers a fortnight ago.
And Coates is eager to repeat the feat and emulate Reds defender Martin Skrtel by becoming a goal scoring centre-half.
“It was a beautiful goal, but the unfortunate thing was we did not win the game,” added Coates.
“It was a good goal and I’d never scored one in that way before. I scored goals in Uruguay, but never like that!
“I hope I can repeat it again one day – but I hope if I do, we win the match as well.
“I don’t necessarily practice my attacking in training. I think it’s down to whether you’re in the opponent’s area, or not.
“Martin [Skrtel] has scored a few goals this season, and I think it’s about being in the right place.”
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