I recently fell in this situation and found myself hacking a solution. I had an Axis 206 camera which required a 5v supply. I had a supply that would work but did not have the barrel jack for it (it was cut off to be put on a robot. With a few minutes and a stroke of hackgenuity I was able to have the camera powered and running.
NOTICE: If you end up damaging your device either by using a power supply with the wrong rating or by providing reverse polarity then I am not responsible. HACK AT YOUR OWN RISK!
Step 1: Parts and Materials
Device to be powered
Piece of wire about the size of the jack
Power supply with proper rating
Wire Stripper (or if in a bind a knife)
Polarity knowledge of the device to be powered
Step 2: Strip the Wire
Once stripped flare the outer strands and leave the middle 4-8 together.
Step 3: Remove the Middle Strands
I did this in 2 steps. First I pulled out 4 then I pulled out another 2. Your mileage may vary.
Step 4: Press the Wire In
I found doing a rolling motion going from the tips to the flats of my fingers helped give me leverage. If it doesn't go in you will probably need to remove a couple more strands.
Step 5: Make the Outer Connection
Once flat and even press the twisted end into the jack on the OUTSIDE of the wire.
You may need to slightly move the wire over to squeeze it in. Use the pressing technique on the last step if you need to.
Step 6: Testing Time
0 ohms = short - the outer wire is probably touching the inner wire.
Open Connection = one or the other wires is not making a connection
WARNING: Providing the wrong polarity could damage/destroy the device or even cause a fire. Make sure you have the polarity correct. If you do not know the polarity do not attempt! I am not responsible for damages!
Now with the proper polarity in mind (most devices I have encountered had the center positive) connect the wires to your power supply. I used a couple alligator leads to easily connect the two.
If the device comes on then congrats! You have hacked the barrel jack!
Step 7: Some Cleanup
I chose to use some electrical tape to wrap the bare wire as well as hold everything together.