You can use an wireless access point to do this. You will not need any wired connection. Install the access point upstairs. And then configure it to connect to the router at downstairs router wirelessly. I have used many access points to do this. Linksys, D-Link etc. I used Linksys WAP54G. Any access point will do. You will have to make the name of wireless network same for the access point. The access will connect to the router. Laptop will connect to the access point. Make the following items same for both access point and router:
1. Name of the wireless network
2. Security: For example WEP, WPA2-PSK, etc and also the key.
The mode of the access point need be changed to repeater.
Before you buy anything download a manual for any access point from manufacturer website. Linksys, D-Link, Netgear and many more. There is clear description how to configure an access point as repeater.
Hope this helps.