Many thanks for your post to the Ireland Reaching Out message board.
The source that I have checked for you is one that you should take a closer look at:
Landed Estates Database of Ireland. www.landedestates.ie
In particular, the Bateman family is mentioned in the link below and you will note that John's name is mentioned along with his brother Thomas and Rowland. At the bottom of the link are a list of resources for further information, and you might note that there appears to be some archive material in the UK. In addition, there are other links and I see a link in Private Collections that deals with the Bateman family (very bottom).
If you have any further questions, please let me know. You can email me at: email@example.com.
The very best of luck with your research!