They did not convict him: he pled guilty to a crime he was not guilty of in order to try to get a lighter sentence for the real crimes he could have been convicted of. As Constitutional scholars such as Alan Dershowitz and others have asserted, Cohen’s plea to violating campaign finance laws is a horrible miscarriage of justice. No one has ever been convicted under the strained interpretation of campaign law that Cohen pled guilty to. Go back to the John Edwards case. The government couldn’t get a conviction then and the facts were far more damaging to the defendant. Even more favorable to Trump: he asked his lawyer to make payments under a non-disclosure agreement and relied on his lawyer to make sure they were done legally. Many members of Congress have had the government make payments during election years under nondisclosure agreements made with victims alleging sexual harassment. Not a one of them has been prosecuted for campaign finance violations though arguably their offenses are far more serious. Critically, if the payments to porn stars had been reported as campaign expenditures, they would not have been illegal under campaign finance law and would not have been known until after the election. Lots of campaigns, including Obama’s, have failed to make timely disclosure of campaign expenditures and have ended up filing amended statements and paying fines.
A key point is that Trump has paid settlements in connection with non-disclosure agreements numerous times over many years.
The Cohen plea is evidence of nothing more than prosecutorial misconduct.