Yes, with certain conditions. In the Zoning Ordinance (PDF), this use is classified as a care center/daycare center or family day care home, depending on the age, relation, and a number of children being supervised.
Family day care homes are defined as a private home in which one but less than seven minor children are received for care and supervision for periods of less than 24 hours a day, unattended by a parent or legal guardian, except children related to an adult member of the family by blood, marriage, or adoption. It includes a home that gives care to an unrelated child for more than 4 weeks during a calendar year. These family day care homes are permitted in all residential zoning districts.