Lock Tim Swinson comes in for the injured Jonny Gray while Ryan Wilson starts at number eight in place of Josh Strauss who drops to the bench.
Peter Horne, who impressed after replacing the injured Russell early in the France game, stays on the bench with Cotter opting to partner Weir with captain and scrumhalf Greig Laidlaw.
"We were pleased with our sustained effort against France," Cotter said. "I was happy with the way we adapted to losing Finn so early in the game.
"The challenge for us now is to keep constructing our game and enjoy the last coming together of the championship in a Scotland jersey against an Ireland team full of confidence after a convincing win over Italy."
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If Scotland beat Ireland it will be only the second time since the start of the Six Nations, and the first time since 2006, that they have managed three victories in the championship.
The Scots lost to Wales and England before beating Italy 36-20 to register their first win in the tournament for two years, ending a nine-match Six Nations losing run.
Cotter's men followed up by defeating France for the first time since 2006. Scotland have won in Dublin only once since 1998.
Team - 15-Stuart Hogg, 14-Tommy Seymour, 13-Duncan Taylor, 12-Alex Dunbar, 11-Tim Visser, 10-Duncan Weir, 9-Greig Laidlaw (captain); 1-Alasdair Dickinson, 2-Ross Ford, 3-Willem Nel, 4-Richie Gray, 5-Tim Swinson, 6-John Barclay, 7-John Hardie, 8-Ryan Wilson
Replacements - 16-Stuart McInally, 17-Rory Sutherland, 18- Moray Low, 19-Rob Harley, 20-Josh Strauss, 21-Henry Pyrgos, 22-Peter Horne, 23-Sean Lamont.
(Reporting by Simon Jennings in Bengaluru; Editing by Tony Jimenez)
