1) A private limited company can buy agricultural land provided it is used for agricultural activities.Since the purpose is dairy farming which is allied agricultural activity there should not be any impediments. It doe snot matter that one of the share holders is an NRI.
2) It must be borne in mind however that there must be approved provisions in the Articles of the Memorandum of Association of the Pvt. Limited Company or make such provisions thereof to accommodate agricultural activities.