Coppino was born to a poor family in Alba, Piedmont, where he later died.
He was professor of Italian literature at the University of Turin and rector of the same from 1868 to 1870, when he moved to Rome (which had been declared capital of the Kingdom of Italy) to follow his political roles.
Coppino participated to the elections for the Chamber of Deputies of the Kingdom of Sardinia for the first time in 1857, but was defeated at the ballot.
He was subsequently a member of the Italian Parliament for some 40 years, interrupted, and twice President of the Chamber (both times succeeding Domenico Farini).
Laws issued during his tenure include one for economical support for teachers, reorganization of kindergartens and of classic instructions.