In 1939, Konyha was elected president of Local 11800 and business manager for the Cleveland District Council of Carpenters.
He resigned both positions in 1970 when he was elected a vice president of the international Carpenters union representing District 3.
After the retirement of William Sidell in 1979, Konyha was elected his successor as president of the Carpenters union.
In 1981, Konyha invited President Ronald Reagan to be honorary chair of the union's 100th anniversary celebration.
In the interim, Reagan asked Congress for tax cuts and fired striking federal air traffic controllers.
Nevertheless, the bad blood between the two men did not prevent Reagan from appointing Konyha to the National Productivity Advisory Committee later that year.