Grandfatherliness

[…]; the collector’s voice gradually deepened over the years to a granular, all-forgiving grandfatherliness.

Source: wiktionary

Past presidential styles have varied from the laconic leadership of [Calvin] Coolidge, to the calm grandfatherliness of [Dwight D.] Eisenhower, to the boyish exuberance of [John F.] Kennedy.

Source: wiktionary

At the front counter, Archer bought two Cokes. The glass kind, he said when I came up beside him. He spun the bottle in his hand, and I figured he probably wasn’t allowed to drink Coke. Far as I can tell, that’s what relationships come to—a giant game of what can I get away with. They’re the best I said, and he offered the second bottle, and I took it. A touching gesture of grandfatherliness, or I’m being cynical.

Source: wiktionary