BUT I AM WORRIED THE KIDS COULD BE INJURED!

You cannot deny tenancy to prospective tenants just because they have children, even if you think the rental property is unsafe for children.  Families are a protected class, so even if the property is such that owner could be assuming potential liability by renting to a family with children, the owner cannot deny tenancy on that basis. For instance, if an owner doesn’t want children in a houseboat because of concern that a child might fall off and drown, that decision is not the owner’s to make and denying tenancy on that basis would be considered a discriminatory act.