For the purposes of this question, I’m limiting “opposite party” states to states that were more than 5 points for the dominant party’s Presidential nominee in 2020. In that spirit, I am excluding close states like Nevada, North Carolina, and Georgia. So for this exercise, the current opposite party governorships are
For Republicans:
Vermont (Biden + 35)
Virginia (Biden +10)
New Hampshire (Biden +7)
For Democrats:
Kentucky (Trump +26)
Louisiana (Trump +19)
Kansas (Trump + 15)
My initial thoughts on this are that the most likely options would be somewhere like Oregon, South Carolina, Alaska, and Maine. I think there might be an outside shot at Mississippi later this year, but it is unclear just how exactly unpopular Tate Reeves is, although Brandon Presley has the kind of profile (on paper) that might be able to take advantage of an opportunity there.
Vermont is lost after Phil Scott stops, Virginia actually has hope to stay R if another Youngkin R runs (and Youngkin ran the state well as it seems as of now). NH is wjatever.
Kentucky seems to be a D hold while the other two are both flips.
New York seems close to one considering 2022 results. Maybe Iowa or Ohio could get a moderate D.