This is a tough one, because it's called a Relay Station. While that might be an American term, I don't think a coach house is the same thing, because that appears to be a storage area, usually on an estate, sort of like a garage of the times. The relay station is specifically to exchange the horses. Just as a note, I did see it in the context of The Pony Express a lot, but that certainly would not be the only usage of a relay station, and the Pony Express didn't exist in the Middle Ages.
Unfortunately the buildings are not listed in the rules. I had to find a played game to find the context of this. I do wonder if someone has the original French game to see what this building says. I'm not sure it matters since it's an old term. I had a heck of time trying to find information cause "relay" comes up with too many other modern things.
So I looked to the origin of the word instead, to see what can be used to translate it. The word "relay" in and of itself is meaning to trade off in some way, an exchange. So that's how it got to be used for the kind of relay you have in a race, foot race, swimming race, etc. The person is traded off for the next person (or next team). So it does apply in a similar fashion to trading off the horses. It comes from the French word relai, which is from a Latin word that means "to slacken" (laxare). I don't get where "slacken" fits in.
If you can translate the word like a relay race, it might work. Unfortunately relay as a verb also means to give information from one person to another, like "I'll relay that information to my boss." It also has an electronics meaning. I'd hate for anyone to translate into one of those.
The word "rural" is a little meaningless because most of the world was pretty rural. So the word seems a little redundant to me.
Since it's just a game, you might have to just use what will work. If you want to be picky like gamers tend to be, you could try to research what those were called in your specific language. Otherwise, you could get away with using "stagecoach station" even though it's not entirely right. (Or the horse exchange, or whatever your imagination can come up with.) In the end, can anyone tell from the picture of the half-built building what it's supposed to be?
