Yes, I know of a home on the 9000 block of East 136th St South in Bixby. It has .76 acres, 1921 Sqft, with many updates. There is no HOA. It is between Memorial and Mingo. It is not listed anywhere at this time and would be willing to do a FSBO.
I don't know if anyone answered your question about the house in Jenks or Bixby on the acre but there are several great homes that would fall into that criteria. Knowing the ballpark price you are wanting to purchase in would be helpful in directing you to the right areas as well. I would be happy to send you some info if you want to list some additional criteria you are looking for as well as price. There are some great deals right now!