After much tedious experimentation, I am convinced that, in the Boy version of the game at least, the Third Rival Heart Event cannot be experienced before the second year. This actually makes sense and is true to general principles of Harvest Moon. The game ALWAYS gives you an advantage over your rivals and HM Boy & Girl is no exception.
The 3rd Rival Heart Event in the Boy version is a two-part event in each case, rather like Skye's Events in Cute. Part I and Part II may occur in the same location but usually occur in different locations. In some cases, you can trigger Part II on the same day as Part I. I initially intended to name the event the 3rd and 4th Rival Heart Events but I soon realised that they really were connected and formed a single event.
For example, in Elli's 3rd Rival Heart Event, Part I occurs at the Beach, where the Doctor tells her that he feels he is ill-equipped to run the Clinic as most of the 'business' is related to childbirth. He speaks of leaving Mineral Town to study elsewhere. In Part II of this Event, you will find him in Confession at the Church. He will continue much in the same vein, while Carter will speak of his own insecurities but ultimately declare that he has to look within himself and stay in Mineral Town only if it serves his own needs to do so.
Another reason not to label these events as the 3rd and 4th Rival heart Events is because the marriage of the rival does NOT follow after triggering Part II of the Event. There is another Rival heart Event that must be experienced before the rival will marry the girl. I am beginning to suspect that the 4th and final Rival heart Event cannot be triggered before the 3rd Year, but I could be wrong. If any one has been able to induce a rival to marry in the 2nd year, please let me know! Ultimately, I will return to my Boy game and trigger all the rest of the events myself but in the meantime...
I must return to my very difficult life as a girl.