It's pretty simple: cut the connector off of the original battery pack (the one that holds 8 AA cells) and solder on your favorite connector to the just-cut wire. I picked JST because it was small and didn't take up much room in the case.
article on swapping out the battery. It's a comprehensive solution, and involves resoldering the motherboard.
The method presented here is a lot simpler. You don't have to touch the main board, but you lose the low voltage beeper. That means it's possible to discharge the LiPo battery below 3V/cell. You just have to be careful at the start of the day to have the battery charged to 10V or more.
Be careful when soldering your connector not to reverse the polarity. There's no polarity protection on the motherboard, so if you get it wrong you'll fry your unit!
That being said, it's working well for me.
Update: the old battery I was using started having problems with one of the cells. I didn't have another conveniently sized LiPo, so I replaced it with a LiFe battery from HobbyKing. Notes on that are here:
Update: Javio left me a great comment on diydrones that goes into detail on how the LM7805 voltage regulator works:
There is a little confusion about the best 2S vs 3S better battery for the 9X. If conceptually it is true that a bigger dropout voltage between input and output leads in a bigger heat dissipation, the 7805 regulator has been designed to give the best performances with a differential voltage between input and output of about 5 to 10V. With the 7,5V (from 6V depending on the model) minimum input required voltage (2,5V of differential dropout voltage between input and output for 7805) the output peak current can not be achieved (the regulator can´t work at full dynamic range). In fact the factory testings of the LM7805 are done with a typical input voltage of 10V. Following this lines, and assuming that the input regulator is a 78xx, a 3S Lipo battery should be a better candidate than 2S to power the turnigy 9X. You can check the Peak Output Current Vs differential input-output voltage characteristic in the figure of page 21 of the attached datasheet or the Droupout voltage characteristic googleing "7805".
This explanation does not means that a 2S is a bad option, but in this case the regulator won´t work at full dynamic range of its output current. By the way, looking the datasheets a dropout of 5 to 7V between input and output (corresponding to an input voltage between 10 and 12V) doesn´t lead in a significative amount of heat increase.
Cheers from Spain.