It would be discrimination on the basis of age to refuse to rent to tenants under the age of 21.
A tenant at least 18 years old has the right to rent an apartment. However, you could screen-out tenants using who don't meet certain criteria such as good credit, positive tenancy references and history of full-time employment. Have all applicants complete a rental application.You should also have lease provisions which prohibit parties. Protect yourself by charging a large security deposit. Consult with an attorney for guidelines on screening tenants and using leases.