Although he gives no history of them, you could take a look at Will Ackerman tunings page, where he gives a few of the tunings he uses on a Martin parlor.

I copied the following quote from this page Here, the author also gives a comprehensive list of tunings for every stringed instrument imaginable except the parlor guitar:

"PARLOR GUITARS are very similar to Baroque guitars, with the exceptions that their tuners are usually mechanical, after about 1820, and the lower bout of the body is a bit larger than the upper bout. I would accept these as a reasonable attempt at using a period instrument, so long as gut or nylon strings are used. If you own an old Model 1887 Washburn, this is what you have. WARNING: many of the American made Parlor guitars have "pin" bridges the same as on modern steel-string guitars. If you use steel strings on these old parlor models, you will ruin them. They are made for gut or nylon strings ONLY!"

Joe Wilson in his article Masters of the Steel String Guitar discusses, briefly the emergence and popularity of the parlor.

It's all I can find at the minute.
Good luck

B.