LorettaNJ said:True, if you disturbed the root ball while repotting, you could have stressed it. And if you just dropped the root ball in another medium, sometimes the water goes around the roots, especially if it was dried out coir or peat and the new soil is moist. I've had to break open root balls in the past to get out whatever junk it was grown in.
There is no way you caused root rot if you watered once. Coleus can take wet feet for quite a while. Instead when I look at your cutting, it looks like it is a bit stingy in length. If it doesn't bounce back I would suspect a greenhouse plant that wasn't hardened off and doesn't have a lot of roots. You could place the whole pot inside a plastic bag, not completely closed off and see if you can get it to bounce back that way.
LorettaNJ said:Coleus can have a slow death like that and it is usually from the stem and roots. But also, you just have it two weeks. You trimmed off the wilted leaves, you put outdoors in good moist soil, so all you can do now is wait as Arlene said and hope some growth shows up. If not, get another coleus. I have had coleus in your state before. Some make it and become beautiful plants and some not.