I don't see any Ainley's that would fit until 1880. On the 1880 Randolph Co. census there is a Richard and Joseph Ainley with families. Both men born Indiana, their father born England and mother born Indiana. On the 1920 Randolph Co census there is a William Ainley living as a boarder, age 81, widowed, that was also born Indiana with parents born same locations as Richard and Joseph.
If you don't have this info, let me know and I will send it. I am not related, just doing research in Randolph Co. and saw your query.