Tappan series 110 gas range
Takes about 15 minutes to fix. You will need a philips head screwdriver, pair of scissors and a butter knife. What you're going to do is cut the wire to the beeper. Your clock will still function.
Start by removing the glass faceplate that encloses your clock. By removing the 2 screws on either side of the metal housing, you can remove the faceplate (you'll have to remove the clock's pushbuttons, but that isn't hard, either. I used some spring-loaded pliers to get a good purchase, then pulled straight back. Oh yeah. You need pliers, too. Don't worry, you won't break the buttons; they'll snap out and push back in, later). Use the butter-knife to carefully work the glass out of the metal frame. The actual clock is secured by a couple more screws, which are easily removed, once you've removed the abovementioned faceplate.
[The clock, btw, is made by Fridgidaire (part # AP2125434 ), in case you want to replace it. Costs more than $130(!)]
If you haven't already unplugged the stove, now is a good time. Do not touch the two metal connectors of the two most prominent wires on the back of the clock, when the unit is plugged in! Yes, it's the voice of experience, talking...
You will notice, when you're looking at the back of the clock unit, a small metal disc, enclosed in plastic. If you plug in the stove, and listen, you should hear the beeping coming from this area. There is a medium-sized hole in the middle of the plastic housing, allowing access to the metal disc. There are two very small wires, red and black, leading into the housing and attached to the disc in two places. One wire is attached to essentially the center part of the disc. The other wire (in my case, the black wire) is attached rather toward the outer edge of the metal disc. The outer edge is even a slightly different color, so you can identify the two parts. In my case, the sound was emitting from the outer edge, as opposed to the center portion of the disc. If you press a Q-tip against the center portion of the disc (thru the hole in the plastic housing), and the beeping continues, unchanged, the sound is probably coming from the outer edge. You can check by bending the Q-tip, and working the tip over to the edge of the metal disc--by applying pressure, you should hear the sound change, slightly.
Unplug the unit, and cut the wire that corresponds to the part of the disc the sound is coming from--that should solve the problem!