San Carlos Borromeo de Carmelo was a prominent mission, headquarters of the mission chain during Fr. Serra's life and located near Monterey, the civil and military headquarters of California. Accordingly, the mission was sent a significant number of religious objects and "church equipment." The Spanish authorities also decided to build a special stone church at Carmel and sent an architect / master stonemason, Manuel Estevan Ruiz, to build a the present church (between1793-1797). Ruiz designed this church to have two bell towers and you are right, the larger one contains nine bells, most of them original.
My friend Donald Toomey, a noted California Missions author and special expert on religious art tells an interesting story of the history of the Carmel bells, drawing upon research that Cora Fremont Older did and published in her 1938 book California Missions and Their Romances.
It seems that during the beginnings of mission restoration in the early 1920s under the leadership of Fr. Monsignor Ramon Mestres, only one of the original bells was left in the tower. It bears the inscription St. John of the Cross 1781. Fr. Mestres found two of the missing [original Carmel] bells in Watsonville, where they had laid for 63 years. Another bell, cast in 1690, was given to Carmel in recent times (exact date unrecorded) by George Barron. Another Carmel bell, with Spanish marks bears the date 1805. Two other bells in the tower came from Russis (dates unrecorded).
So while we now know more about the origin of the bells to my knowledge no one has a definitive answer for the number. As Mr. Toomey wisely states "the full story of the belkis of Mission Carmel still remains undeciphered!"
My own hypothesis - and it is just that - is that the number of bells was determined in a later phase of the restoration, in 1930s, and chosen to honor Fr. Junipero Serra, who founded the first nine missions.
If you don't have it you might enjoy Mr. Toomey's book The Spell of California's Spanish Missions. It provides considerable detail on the Saints for whom each mission was named and on the religious art found at each mission.