I spent some time on the phone this morning with NH Fish and Game.  I can't legally use a Conibear trap without risking incurring some hefty fines if I catch a non-target animal.  I was also informed that there is a big study going on right now regarding the prevalence of bobcats in this area, so there are several animals that are carrying sensors on their bodies for tracking purposes.  
The recommendation was to use a Have-A-Heart trap to catch whatever has been plaguing my birds.  Once the culprit is caught, F&G recommended that I relocate and release the animal 10 miles from my home.  I will say that again because I am still just floored by this- relocate and release 10 miles from my home.  I was sputtering on the phone, "What?!?  Isn't relocation illegal in most areas for very good reasons?  Why would I dump my problem animal on someone else's doorstep?"  The warden was very clear that relocation is their choice method of removing problem animals.  The warden stated that the animal needs to be relocated to a wooded area and not a residential neighborhood.  I wanted to say, "Hey sweetheart, I live in a wooded area where people dump their unwanted animals.  I get to see firsthand what happens to these displaced creatures.  What the heck kind of policy is that?  Allow me to tell you, it is a terrible one."  I didn't actually say any of this to the warden, but I really wanted to.
It becomes clear to me that I am going to get no help from F&G.  The only kind of intervention they are going to offer is a fine if I catch a stupid bobcat, which is entirely possible.  I did get a list of certified trappers in the area, so I need to decide if I am going to risk getting into trouble for trying to trap the problem myself or spend money that I don't wish to spend having someone come out to do it for me.  I wonder if the trappers are just going to release any animal they catch into another person's backyard.
So frustrating.