You need to have a very well defined idea of when and where the person filed the application.
The records can be kept on a county level, in a state historical archive, at a district level, those are some of the choices.
You start with the State the person filed in, to see how they handled those archived records. You might be surprised what you can turn up by googling.
>>Thomas Keane, according to the 1920 census was naturalized around 1889.<<
What do the 1900 & 1910 Census have? Is the data consistent?