Hi Om,
Do you have a signal that marks the start of your coincidence window? If so, you could set your scope to trigger on it, set the trigger position to 0% (all the way to the left) and then set your time/div to capture for the length you want (let's say you want a 50 ns window, you'd set the scope to 5 ns/div, or a little more) and set the trigger to norm mode, that way the scope will only capture when it receives a trigger signal as you defined it (in the trigger menu).