Possible spelling variations of this name are Parleman and Parliman.It is possible that the branch of the family you are looking for is possibly Abraham Parliman (1777-1860) and Rachel Van Steenburgh (~1791-<1850) m 5 dec 1812 New Paltz, Ulster Co., New York.
This family, along with some of Jacob's brothers moved from Ulster/Orange Co., New York areas to southern Michigan, specifically Jackson and Van Buren Counties.And are seen in census records to move between New York and Michigan.
This is where I would start to look.It is very hard to research this family, though.The names Parleman, Parliman, Parlaman, Parliament and Parlemon are all valid spellings of the name as recorded in public records.It is hard to be specific as to what name any did use.
I find as I research, if someone has a Parliament surname, I may have the same person listed with a Parleman surname.I guess as literacy became more prevalent, people settled on a spelling they liked or were known by.
However, there are other Parliaments who settled in the later part of the 1800s to Ogemaw Co., Michigan, area.This branch of the SAME family is descended from George Parliament, a loyalist who fled to Canada during the revoluton.This particular family will predominately carry the name Parliament.
If your research is taking you back to Orange Co., New York, you may have better luck using the Parleman or Parliman surnames.
I cannot make a match with any names you have given, though.