Anime can be a strange place just because of being unfamiliar with the culture. I have just through osmosis learned a lot about Japan and other Asian cultures but there are still things that elude me. In this slight, though cute, little anime I really don't know what the significance of the deer is. I've seen deer in other temple settings before (Latest was the talking deer in Judge Dee), but I don't know WHY they are there. What is the story behind it? I just don't know.
Coicent is set in the future. There's a big festival and our hero is hoping for a little fun and maybe meet a girl. Being a typical Japanese Nerd type he's going to need help. So a talking white deer takes first his bag and then him on a wild ride. It just so happens that on that ride a girl literally falls into his lap. She's escaping an irate (if not necessarily evil) corporate boss and she's some sort genetically enhanced being. Between the two of them they fall and love and have adventures as they try to keep away from corporate goons.
It's a light little tale but it is fun and well animated. Oh by the way, "Coicent" is a corruption of the original Japanese title "Koi Sento," so its not some weird mispelling of coincident or something like that.