What child seat would fit an old model Gary Fisher bike?
Your bike has cantilever brakes, which use a straddle cable and then the main inner cable pulls that.  Totally typical brakes for the age of the bike, and perfectly serviceable.   However the center cable has to run straight up to a hanger, and its not impossible that some brands of seat may foul this area.

Not quite sure what pins your LBS is referring to. The full-sized image clearly shows two lugs for mounting a rack (on either seatstay, just by the brakes.)  The photo cuts off at the bottom but you definitely have one lug on the dropout where the mudguard currently mounts.

Could be the bike shop was referring to your front derailleur cable, which is the wire going straight down the seat tube.  That could interfere with the clamp used in the next image.

So depending on your budget a rear mounted seat like this should work.

This one uses a permanently mounted clamp on the seat tube (black, behind rider's left knee in photo) and the two silver poles are the main supports for the child seat which is held suspended over the rear rack.

Downsides - the view isn't great for a kid, and they're always looking sideways which is bad for any kind of accident.  The rider can't see the child.  Also note the child's weight is more behind the rear axle than in front, so this unweights the front wheel a bit and makes the bike handle worse.

Also notice the rear tyre may just be low on air, but it also shows how much the weight balance is altered.  Adding a 5-10 kilo child plus a seat all on the back wheel is not ideal.



Personally I'd strongly recommend a mid-mount seat like this



Notice the child can see what's coming, and can hold the sleep pad, or can even fall asleep on it.

The downside is that the average and taller riders will have to ride slightly more bow-legged.  Most models do allow the seat to be easily removed leaving just a mounting bar in place, at which time the bike rides normally.

Some further reading for you:
http://www.bikeradar.com/gear/article/best-child-bike-seats-39715/