As you probably have already learned, the missions varied in size. San Carlos Borromeo de Carmelo was one of the most prominent missions but the neophyte population was smaller than the average. There were only 876 neophytes at Mission Carmel in 1795, twenty five years after the mission was founded, and this was the peak year. By 1832, the population had declined to 185 (this was the year the mission was secularized). Unfortunately the Europeans introduced many diseases (like small pox) to which the Indians had no immunity.
The children were particularly vulnerable. Sadly, over half of the children born on a mission died before reaching age 4 and only about two of every ten lived to be teenagers. The families lived in small rooms in generally unsanitary conditions. The children who lived at the presidios (forts) or on outlying ranchos had a higher chance of surviving.
The children at the missions did do things children do to have fun. They played games, generally games learned before the arrival of the Spanish. They were instructed in the Catholic faith and taught Spanish but at a relatively young age they began to participate in the work of the mission. The girls helped their mothers with cooking and cleaning and making clothes. They boys worked in the fields. At many of the missions there were choirs and the young boys were taught to sing.
In her book Grass Games & Moon Races Jeannie Gendar describes many of the games played by the children and points out that "children everywhere can have fund with the simplest 'toys; given the chance”. So it isn't surprising that children made balls of natural material (such as tule fiber or rounded pieces of wood) and played stick games with them. They played variations of games we know today, like hide and seek, tag etc. Whenever possible – particularly in early decades of the mission era - they continued things that they did before the creation of the missions – they gathered acorns with their mother, they went swimming, they visited relatives in their villages
The adult neophytes didn't have a lot of free time but they also played games in their leisure time. Sometimes they played games on which they could bet. If they could get away to fish and hunt they would do so.