Here's what I found:
The male style fitting is called a 1/8" double compression fitting. Weatherhead, Edelmann, and Everco all offer replacements for these special fittings.
According to the manufacturer when using plastic tubing use internal tube support, that is so the compression sleeve squeezes tight against line and then internal tube support for a leak free seal. I'll post additional pictures when I get all the parts together. $1.15 a piece on line for the 1/8" double compression fitting.