There is a discussion here about solutions for external power for the TX-1 (which uses a NB-4L battery).
Basically the best and easiest solution is to just buy the external Canon DC power supply. Your manuals should tell you what the part number to look for is.
If you want to save yourself some dollars (at your own risk of course - and cost you some time), then you can make your own if you know how to solder a few wires and know how to get + and - the right way round. In that case you need to make your own "fake" battery, and get your own wallwart power supply (or external battery pack). I think anything from 3Volt to 4Volt should be fine. A 1Amp supply is probably OK (especially if you are not using the flash), but a 2Amp would be great (I have to disagree with Mariush, increasing the maximum amps is not a problem within reason: the camera only takes as many milliamps as it actually needs). You may have a 3Volt adapter around for an old cellphone that will fit the purpose perfectly. Make sure any supply is DC (says DC or has a long bar above 3 short dashes next to the voltage). I think databoy is scaremongering. Sure, don't buy an unsafe power supply... but anything you can buy from a reputable supplier in the US will be fine (litigiousness at least tends to make suppliers a bit conservative!). If you do need to buy a supply, I suspect the easiest to find would be a 3.3Volt supply used for hobby electronic projects. The camera electronics can handle a fairly wide range of input voltages (as shown by CHDK battery voltage indicator!).
Good Post robocat! I found this very good discussion on power supplies and wanted to add my findings as they may be very helpful for others. I had to do a 10 hr timelapse and needed reliable power for my Powershot A590. (The A590 requires 3.15V/1.5A)
So I bought a 'Powerline' 1300ma Universal supply (at Walmart ~$18.00) and thought I would be all set--no way. I tried it at 3.0V and the supply whinned quite loudly. So I tried it at 4.5--thinking surely it should be able to pull the .2A from the increase in voltage. Not the case! It still whinned loudly--piece of junk.
I would have bought a AC-K800 from ebay, but didn't want to pay $30-40 overnight shipping, as I needed it quickly. Alas, I found the Dynex DX-UA at Best Buy ($26) and let me tell you; very happy. It has a 2 stage system, with amperage clearly stated for each voltage!! Imagine that?! I chose the 3.3/2.1A and I hear no noise from the supply and the camera works beautifully.
Awesome that Dynex got it right!