Once you select a mateable cat (There are threads that give more detailed info on what cats are what, and what they like for gifts), You give them their most loved gift, 3 times a day. Once they have 5 full stars, Coco will appear to tell you about the Ritual of the Red Rose.
Actually, Coco tells you about the rose on Autumn 5th, year 1. If he/she has not told you after then, try sleeping at night. It helps! I played this game with all the saves, and he/she told me no sooner than that day. Sorry if this is old, had to make sure people knew.