To make convivial; to create an atmosphere of conviviality and sociable enjoyment.
From convivial plus the suffix -ize, which turns adjectives into verbs meaning 'to make' or 'to cause to be.' The -ize suffix is one of the most productive in English.
Convivialize is a very rare verb—most people would just say 'make convivial'—but it shows how -ize allows us to nominalize almost any adjective. Though not common, it's perfectly understandable to any English speaker.
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