Further info - Charles RICHARDS 1st was a Loyalist from NJ according to the Loyalist list in E.C. Wright's book - Loyalists of NB. He was the only RICHARDS who settled in Greenwich. As for Thomas, I found that he married Maria Barbara HAMM d/o Loyalist Andrew HAMM and Maria Barbara BARAGA on 7 May 1828 - Dan Johnson's newspaper extracts and marriage records mentioned below. This is further backed up by the 1851 census of Greenwich which lists the families of Charles age 47 m. Jemima, Joseph age 45 m. Mary and Thomas age 81 m. Barbara.
From Ruby Cusack's transcription of Marraige Register "A" of Kings Co.....
Charles Lewis RICHARDS / Jemima ELizabeth JONES 10 Feb 1831 Wit: Joseph RICHARDS & Samuel JONES.
There are no other male RICHARDS married from Greenwich and I can find no other mention of an elder RICHARDS so although I hate the word "assume" , I think it is safe to assume C.L.'s father was Thomas by the process of elimination. If you ever get to the PANB they have the baptism records of churches in that area on microfilm.
You probably have this list but just in case, here are the RICHARDS ( mis-transcribed as REICHARDS) in the Kings Co. Probate index. Again, Thomas is the only likely one.
REICHARDS: Charles 1800
REICHARDS: Charles L. 1875
REICHARDS: James N. 1900
REICHARDS: Joseph A. 1854
REICHARDS: Thomas 1853
REICHARDS: William D. 1904
Hope this helps,