You just need a rear wheel with a fixed hub which has a cog and lockring.

Here are some wheels from Sheldon Brown's store: http://sheldonbrown.com/harris/wheels1.html#622
You will also need a cog and lockring: http://sheldonbrown.com/harris/fixed-sprockets.html


Check to see if the current wheels are 27" or 700c. If the original wheels are 27", you should avoid a 700c wheel since you don't have enough room to move the pads down adequately to contact a smaller diameter rim.