She argued 'convincingly' [='persuasively'] that more money should be given to public schools.
There is no 'convincing' evidence to support his theory.
Your argument/story isn't very 'convincing'.
(..) are indifferent to the trials of young love. - # The wishing well # - Armed with warnings and doubts, Noah and Allie gave a remarkably convincing portrayal of a boy and a girl traveling down a very long road with no regard for the consequences. They fell in love, (..)2004 The Notebook