I have a set of cordless headphones, but I've lost...

The specifications for your power cord would be listed on the unit itself if not in the owner's manual. If you look around the unit near the area where the power cord plugs in or if you look on the bottom there will be some sort of requirement that says something to the effect of "12VDC or 15VAC etc." or whatever the voltage and miliamperage is required to power it. Then you can take that information to Radio Shack or some other electronics retailer who can help best match a power supply for the unit. Also you could contact the manufacturer on their website. Most times they keep things like that as extra stock to sell to customers who have a situation like yours.
After that if all else fails, get a universal power adapter. and start with the lowest voltage and gradually move the switch to the next higher voltage. If that does not work, switch the polarty of the adapter and start from the lowest voltage again until it works for you.
A device like that usually operates anywhere between