Family trees on Ancestry.com say (and census records seem to bear it out) that James' father was Andrew Jackson "Andy" Toy and his mother was Amanda Jane Hatton. Both James Toy and Alice Williams were from Bath Co., Kentucky. Of course, you would need to do your own research--those trees may be incorrect.
I have no idea why they came to Kansas unless it was the reason most other immigrants did--to obtain cheap land. James and Alice appear on the 1885 Kansas State Census in Sugar Creek Twp., Miami Co. However, they returned to Bath Co., Kentucky and are there on the 1900 census. By 1910 it seems they have come back to Kansas to stay, as they are in Coffey County. They are also there on the 1915 census, and of course James dies two years after that.
Do you know if Alice had a brother named Isaac B. Williams? When James and Alice were back in Bath Co. there were several mentions in the local paper about them visiting the Isaac B. Williams family. Then there was one saying that "Mrs. Isaac Williams and children were going west to Neosho, Mo. (Jasper Co.) to join her husband." That Isaac Williams died in Jasper Co. Mo. in 1930.