I have replaced them without removing the cover and belt on a number of occasions- it is just easier with them off. It would be to your advantage to see where this one is leaking. If the pump is actually bad (as in internal seal failure) I would guess it would be coming from the weep hole in the pump housing. If you had a dry place to pull it in I would probably drive the car until operating temperature is reached and then pull it in, shut it off and wipe everything down to remove any coolant that is evident. After shut down the pressure will usually build up and you can watch for where the coolant shows up around the pump. Sometimes crawling under and looking up is helpful (one case where a missing belly pan pays off!) Are you sure all the hoses are tight? If it is coming from the weep hole it may drip down and run off the back edge of the pulley. If the loss isn't because of bad internal seals you can just purchase a waterpump gasket set.

Randy