You can check the Private Agricultural Engineering Colleges at our page: https://engineering.careers360.com/colleges/list-of-engineering-colleges-in-india?branch=Agricultural%20Engineering&ownership=Private

But none of them have ICAR affliation. But the Central Universities for ICAR Agricultural Engineering Coolleges are:

ICAR-Central Institute of Agricultural Engineering, Bhopal

ICAR-Central Institute of Post-Harvest Engineering and Technology, Ludhiana

ICAR-Central Institute for Research on Cotton Technology, Mumbai

ICAR-National Institute of Research on Jute and Allied Fibre Technology, Kolkata

ICAR-Indian Institute of Natural Resins and Guns, Ranchi

ICAR-Indian Agricultural Statstics Research Institute, New Delhi