I am not a Perryman researcher but I had some extra time.
I believe your Wm. A. Perryman's parents were
William G. Perryman and Mary Heath
Perryman, William & Mary Heath - May 4, 1840 from http://www.tngenweb.org/rutherford/mar1840.htm
I have put copies of the 1850 Graves Co KY & 1860 Massac Co IL entries for this couple in a file for the group(see the left hand column from the groups entry site) in a folder which I named Perryman. Hope this helps. this appears to be parents of W A Perryman as they have a 6 yr old son with that name in 1850 & 1860.
Hope this helps
--- In firstname.lastname@example.org, "perrymandw" <dwperryman@...> wrote:
> My ggrandfather was born Jan 1844 in Rutherford Co., Tenn. (perhaps in Murphrysboro) and was, by 1871, in Marion Co., Illinois where he married Martha E. W. Lynch. He died there in 1898. I need his parents & siblings if anyone has them. By DNA I know the line leads back to Roger Perryman (b. ca. 1708 in N. C.). Thanks in advance for any help.