This selection from the David Rumsey map website collates two types of statistical data from the 1900 U.S. federal census. Firstly, there is the 'density of natives of Ireland' (see below), with the number of Irish born people per square mile mapped.
|Density of Natives of Ireland 1900
Secondly, there is the 'proportion of natives of Ireland to total population', where the darker colors on the map represent a higher proportion of Irish-born people.
You can view both maps at this link.