What should I do about my son who exceeded the time allotted for playing on the computer after I swore that he would not exceed it?

Since your son exceeded the designated playtime, you have broken your oath, and therefore, an expiation for the oath (kaffarat al-yamin) is incumbent upon you. The expiation for an oath is to feed ten needy persons, or to clothe them, or to free a slave. If you are unable to do that, then you must fast for three consecutive days. Allah Almighty says: "Allah will not impose blame upon you for what is unintentional in your oaths, but He will impose blame upon you for what you intended of oaths. So its expiation is the feeding of ten needy people from the average of that which you feed your [own] families or clothing them or freeing a slave. But he who finds not [the means to do so] - then a fast of three days [is required]. That is the expiation for oaths when you have sworn. And guard your oaths. Thus does Allah make clear to you His verses that you may be grateful" (Al-Ma'idah: 89).