The phrase "argued convincingly" is correct and usable in written English.
You can use it when describing someone who presents their case or opinion in a persuasive and effective manner.
Example: "During the debate, she argued convincingly for the need to address climate change immediately."
Alternatives: "persuasively argued" or "made a compelling argument".
It can be argued convincingly that cross-country skiers are over-rewarded at the Olympics.
The whole was rich and smooth, and argued convincingly that French and Indian cuisine can be happily married.
He also argued convincingly, among other intriguing speculations, that the death of Marlowe was the making of Shakespeare.
In the past week or so, Grant's Interest Rate Observer, a newsletter, has argued convincingly that figures in Fannie Mae's own accounts brought its reported earnings into question.
Several thinkers (e.g., the theologian Paul Tillich and the philosopher Karl Jaspers) have argued convincingly for a mythological dimension to all science.
Disabled speakers argued convincingly that they would end up costing the state more, if cuts removed support that currently allows them to work or lead independent lives.
The judge argued, convincingly, that loopholes and exceptions in the mayor's rules would result in uneven enforcement and ultimately defeat their purpose.
Considering this dynamic, John Sides of The Washington Post's Monkey Cage blog has argued convincingly that gerrymandering is not what's behind the rising polarization in Congress.
They not only had the money to cover costs, but argued convincingly that the program would train needed singers and technicians as well as future audiences.
Mix in anonymity what do you expect?" Quite a few, however, argued convincingly that the problem is not, as I wrote, intensifying.
The economist Thomas Piketty, of course, has argued convincingly that the returns on capital will exceed economic growth for long into the 21st century.
