A list of nearly every reference I could find to Joe Girardi making a comment on instant replay by doing a Google News search for "girardi instant replay":
"I would like to see instant replay on balls down the line because the umpires are so far away."
November 6, 2007, discussing the possibility of introducing instant replay for home run calls:
"I actually think it has some value on home-run balls fair and foul. A lot of the parks are so tricky. Seeing when the ball goes over the fence and comes back in and whether the fan touched it or hit the railing behind is difficult."
"I think it would break the rhythm of the game … Where would you stop?"
"I don't know if I'm in favor of it (instant replay) for base calls because I think it just might slow the game down an awful lot… But I think in unique circumstances like yesterday, which we all know doesn't happen very often, it might be something that Major League Baseball takes a look at."
"The thing about expanded replay for me is, could they have reviewed that play as quick as they talked about it? Probably. It's the same amount of time—it may even be less."
"I am not saying we win the game if the call (was) right. I am not saying that. … But in this day and age there is too much at stake, and the technology is available. That's what our country has done. We have evolved technology to make things better."
At first glance, Girardi's comments on instant replay over the years seem fairly consistent, showing an openness to the idea of using "evolved technology" in the game. However, all of the instances I could find where Girardi spoke his mind on replay involved moments that would have benefited his teams if replay was expanded—that is, the blown calls hurt his team and instant replay would have fixed it. The one exception to that is also the biggest: the 2009 ALDS Game 2 blown call by Phil Cuzzi that turned an 11th inning ground rule double for Joe Mauer into a foul ball (and, later, a single). When the bad call went in favor of Girardi's Yankees, he was afraid a review would "break the rhythm of the game."
I would be interested to know what Girardi would be saying today if that was Nick Swisher at second base last night and not Omar Infante. We should expect managers to always back their players and their teams, of course, but it might help the cause of implementing useful instant replay if major league managers were ever consistent on the topic.