I had this problem, but in reverse, i.e when opening the doors. The main alarm unit is *usually* located underneath the passenger side airbag (does the cup even have that?). If it does then you'll need to take the dash off to get to it.
1. There are, iirc, four screws spread evenly across the rear of the dash (in the vent near the windscreen and at the ends near the doors). These need removing.
2. If it's the same as mine there are two more screws on the steering column, underneath a cover. To get to these I had to unscrew two screws underneath the column which release the cover. Once the cover is off remove the two screws near the dials.
3. The dash should now lift off, you may need to lift the rubber seal from around the doors to remove it easily, this just pulls off (and pushes back on).
4. You will be left with the passenger side airbag, this is held on with, I think, two screws. Be gentle when removing this, or you could end up spread-eagled in the rear of your car!
5. Lift out the airbag and there will be a black box with wires plugged in to it. Pull out the wires and remove the black box.
6. Reverse the process to put everything back.
Hope this helps, of course this only works based on the assumptions I've made about your car! It is a temporary solution, but I know how annoying the alarm can be.
