On Familysearch.org There is a birth/baptismal record showing for a Richard Max b. 4 Dec 1868 in Littelton parents names are given as John Max Mary Sheppard. See Link http://tinyurl.com/az6grw6
There is also a Max birth recorded 7 May 1866 in Newport Tipperary to what seems to be the same parents(same names) Max is a fairly rare name so it is possible that the birth of John Max in Borrisokane registration district Year 1865 Vol 18 page 430 is possibly another child. You would have to get the birth cert to make sure. Birth cert applications can be downloaded from www.groireland.ie
a photocopy of the birth entry gives the same inforamtion and costs less.
If you are able to confirm that John Max is of the same family - I would think this is possibly him in the 1901 Census - there is also details of his mother Mary Max that appears to be of the right time period.
This link shows the distribution of the Max surname in Ireland in the 1850's from Griffiths's valuation (a land tax survey)only 5 in Tipperary.http://www.irishtimes.com/ancestor/surname/index.cfm?fuseact...
Hope this is of help