Another AirPort Extreme or AirPort Express could be used to "extend" the wireless signal to provide greater wireless coverage.
There are two methods to do this:
1) Connect the upstairs AirPort back to the downstairs AirPort using a wired Ethernet connection. This yields the best performance by far...and allows you to locate the upstairs AirPort in the exact area where more wireless coverage will be needed.
If you cannot run the Ethernet cable, a pair of Ethernet powerline adapters might be able to send the signal over the existing AC powerlines in your home. This is an "iffy" deal, but it does work OK for some users.
2) Connect the upstairs AirPort back to the downstairs AirPort using wireless only. As you might imagine, there are significant compromises with this approach since the "extending" AirPort must be located where it can receive a strong wireless signal from the main AirPort Extreme to be able to "extend" it effectively.
The usual location for an extending device is a point that is about half the distance from the main AirPort to the general area that needs more wireless coverage. It may be necessary to experiment on the exact location of the extending device depending on walls and obstructions.
You could try method 2) first if you want...it might do what you need....but keep the fallback plan of method 1) in mind, as it may be needed if method 2) does not deliver the performance that you need.