Hi Kurt,
The NCRS Wisconsin Chapter has a birthday calculator on their web site that most people use. Unfortunately their site seems to be down right now for reconstruction.
I don't have a 1967 calander in front of me but May ended with serial number 119747 and June ended with 122214. That leaves 2467 cars made in June. There should be about 22 work days in that month. With an average of 112.7 cars built a day your car should have been built on the 14th work day about in the middle of the afternoon. That would put it somewhere around the 20th of June depending on how the weekends fell and not allowing for variables in production from day to day due to line problems ect.
I think that the serial number is assigned at the start of production so this would be the date your car was begun, not the day it was started and driven off the line.
I hope this helps some.
Tom