This is a bit of a complicated hack, but I have done this and it works.
I use Windows Media Encoder to capture the video of an online stopwatch. I can then drop this video in as a Video Track 2 in the corner.
Once you have captured the stopwatch video one time, you can use it for multiple videos. A lot of work up front, but it can be used over and over.
Media Encoder
Make Videos By Capturing Screens with Windows Media Encoder
Use online stopwatch program such as:
Online Stopwatch
I hope this helps.
Richard
p.s. After I wrote this, I realized that if you are trying to enter the timestamp (date and time) of the original video, that is a different problem.