The engine will not accelerate. Pushing the throttle causes it to cough and miss but it  will not speed up. The carburetor is completely clean and seems to be in good working order. Any suggestions?  

it is it cutting out (what it sounds like) then it may be running too lean.

cutting is a sign of this.
try adjusting the fuel air mixture screw on the carburetor to the left 1/4 - 1/2 turn and see if it doesn't improve.  

OK. I'll try that, but now it won't start at all. I took the carburetor off to check what someone else had suggested that the throttle may be sticking due to faulty cable. But the throttle is working fine and returns all the way down when the lever is released. But now there is no spark. I must have disturbrd a plug or cable when working on the carburetor. So I need to check the wires. I read that you had a wiring diagram for the 110 ATV. How could I get a copy of that?  

here's an very easy way to check which wire connector are loose,if any.  as you try to start the quad grab one connector at a time and jiggle it, start with the wires around the steering head.  

I found the problem with the 110 not starting. I cut the wire ties on the wires bundled on the left side under the seat which contained most of the wires affecting the ignition. Several of the spade type plugs had small pieces of insulation on them which had moved and allowed some of the bare plugs to touch each other. I insulated all the plugs and rebundled the wires with new wire ties to the frame. I unplugged the wires for the rear lanyard kill switch so it is no longer in the circuit. This switch is normally open, so leaving it unconnected removes one more problem area. I hit the starter button and it fired up instantly and has run fine since.  

if it is still bogging down when you give gas try moving the clip down.