Should I add a window unit when the house already has central AC?

[Daniel Read]

I have an old row house that is 100+ years old. Brick walls with a retrofitted central air system that has been installed. Everything works, but the air flow doesn't get to the 2nd floor very well in the master bedroom. The heat didn't get in there well in the winter and now the AC isn't getting in there well in the summer. The tenant would like me to add a window unit in the master bedroom to help cool it down. 

When I went over there last week the room was warmer than downstairs, but not uncomfortably so. It was very comparable to my house--warmer upstairs than downstairs is par for the course during the summer months, IMHO. 

The question then is this: should I pay to add a window unit or is that a comfort cost paid for by the tenant? I.e. Where is the line between a want and a need? In this case, it seems as though the window unit is a want (comfort) without being a need. 

What would you do? Am I at risk of losing these tenants if I don't add the unit?