I'm not sure what sort of user interface you have in mind, but this might be like it:

time = DialogInput[
  DynamicModule[{data = Null}, 
   EventHandler[
    Graphics[{{Green, Disk[]}, Inset["Click"]}, 
     ImageSize -> 
      100], {"MouseClicked" :> (If[NumberQ[data], 
        DialogReturn[AbsoluteTime[] - data], 
        data = AbsoluteTime[]])}]]]

You may want to play with the option WindowMargins etc. to figure out how to place the dialog window where you want it.

Or maybe you want some other kind of interface.

Thanks, Michael. I had not seen EventHandler[]. I do not understand all the documentation for it, but I think it only works in a dynamic module. I want a function that returns the interval. I tried the line below without success.

EventHandler[time, {"MouseClicked" :> start = AbsoluteTime[];, "MouseClicked" :> time = AbsoluteTime[] - start}]