They are found on the 1920 Federal Census for Roosevelt County, NM in the city of Portales, in Minco Twp (ED#156) Page/Sheet 2A where they are listed under the surname spelling of S-L-A-Y-T-O-N.
Willis Slayton is listed as being age 43 (birthyear c1877) born in TN
His wife, Janet is listed as being age 32 (birthyear c1888) born in KS
The following children are listed with them in this census:
Abel, son Age 14 (birthyear c1906) born in TX Blanch, dau Age 10 (birthyear c1910) born in NM Leon, son Age 8 (birthyear c1912) born in NM Woodrow W., son Age 5 (birthyear c1915) born in NM B[rian?], son Age 2 months (birthyear c1919/20) born in NM
An old family letter indicates that there may have been another daughter [name unknown].One daughter remained in the Portales NM area, the other married and moved to Kansas City, KS.
If you have any information on Willis and Janet Slaten or their children, I would be very happy to hear from you.