You may have the ability to justify the installation of a window AC unit if you show them the 55-248.13. section of the Virginia Residential Landlord and Tenant Act (link below).
http://www.dhcd.virginia.gov/HomelessnesstoHomeownership/PDFs/Landlord_Tenant_Handbook.pdf
Section 55-248.13 Landlord to maintain fit premises.
4. Maintain in good and safe working order and condition all electrical, plumbing, sanitary, heating, ventilating, air-conditioning and other facilities and appliances, including elevators, supplied or required to be supplied by him;
The one obstacle you may have is with number 7 of that section which infers that AC may or may not be a requirement because it states "if provided".
7. Supply running water and reasonable amounts of hot water at all times and reasonable air conditioning, if provided, and heat in season except where the dwelling unit is so constructed that heat, air conditioning or hat water is generated by an installation within the exclusive control of the tenant or supplied by a direct public utility connection.
You could also call the VA Fair Housing Office, but I'm not sure if they answer to AC type of questions:
http://www.dpor.virginia.gov/dporweb/fho_index.cfm
File a Complaint - If you think you have been discriminated against or if you have questions about the fair housing laws call us at 804-367-8530 or 888-551-3247. For TDD users, please call the Virginia Relay by dialing 7-1-1. You may also write us at: Virginia Fair Housing Office, 9960 Mayland Drive, Suite 400, Richmond, Virginia 23233-1463. Our email address is
fairhousing@dpor.virginia.gov. Our fax is 866-480-8333.
- Good luck