The type of thing you could use is what is called a wifi bridge. I think that there are a few different ones available out there but the only one that i've used personally was the Vonets VAP11G WIFI BRIDGE i'm sure with more research on wifi bridges you might find a better version (i say that as mine failed after a year i think).
You install the siftware on your laptop/pc either from the disk or you can get it from the vonets website. Connect the device to a usb port (for power) and the ethernet (wifi disabled ofcourse), launch the software when the device has settled and follow the onscreen instructions. Basically you'll get to the point where it searches for wifi signals, you select yours and input your key and connect. The device will then be configured to connect to any device that needs an ethernet connection.
However, this particular device needs to be powered by either usb or a/c, if you can't power it with a usb port there are a/c plugs that have a usb port (different wattage and volts i think so be careful), for a/c power i used an old netgear powerpack as it's the same fitting so either one of those off ebay etc or perhaps a powerpack with lots of connectors might have the correct fit..
The one i had malfunctioned after about a year but they are cheap, it was the most simpleist to set-up. Ofcourse with whatever one you decide to go for, do your research with google AND youtube, something that is truely a wifi bridge and not an extension from a router. The vonets one has an ethernet connector but power..., some might have power packs but no inbuilt ethernet. All i can say is my experience with Vonets.
One thing you also need to think about is your data limits because uploading from the slingbox at several mbps will eat into a data allowance very fast, likewise for the recieving end for downloading.
A certain port needs to be opened to work with slingbox, dunno what you can do with regards to that with a mifi, if it's not possible then you would probably have trouble getting it configured/set-up to work.