Hi Brian,
There's not a single REST API call that will do this; however, you should be able to calculate it with a series of calls.
One possible approach...
Start with getting all of the messages for the specified user in the specified date range. You can do this via REST API message search call, with specifying the user id and the time range as second since epoch. For example, here is a call for all of the messages I've posted on the Lithosphere between now and 1 month ago:
http://lithosphere.lithium.com/restapi/vc/search/messages?q=date:[1346772203 TO 1349364211]&author_id=15
Please note that I've left the query string parameters unencoded for readability, but it's always a good idea to URL encode your query string parameter values.
Once you have the list of messages, you can look at each one for the date of the reply:
<post_time type="date_time">2012-09-10T19:41:55+00:00</post_time>
as well as the root message:
<root type="message" href="/messages/id/59154"/>
You could then make another REST API call to get the details of that root message (such as the author and post date):
http://lithosphere.lithium.com/restapi/vc/messages/id/59154
There may be some additional analysis that you may need to do such as checking to see if the reply author and the root author are the same (user replied to their own thread) or checking which reply is first (user replied to the same thread more than once), but these REST API calls should hopefully give you all the details you need to work with.
I hope this helps!
-Adam
