PAD offers a variety of excellent data services and analysis, and works closely with both the Census Bureau and the NYS Census Data Affiliate Network. One of the things that they offer are population projections for every county in New York. The most recent version of their projections run through the year 2040, and offer breakdowns by age groupings, by sex, and by sex by age groupings.
Below are the two counties' population pyramids - basically a graphic representation of their population age distributions broken out by sex. The initial one in each series reflects the most recent census data from 2010. The successive pyramids are from PAD's projections for the years 2020, 2030 and 2040. Clicking on each will enlarge it to make it easier to see.
Herkimer and Oneida County Population Pyramids (click each to enlarge)
To see the actual data associated with each of these pyramids, be sure to visit the PAD population projection page.