"convincing manner" is a correct and usable phrase in written English.
You can use it to describe a certain way of speaking or presenting a point of view that is effective in influencing others. For example, "Her argument was presented in such a convincing manner that it was impossible to dispute her point of view."
Those two ideas needed to be demonstrated in a convincing manner - so convincing, in fact, that Party leaders could justify overturning the agreed-upon selection process.
He integrates sound economic analysis with historical detail in a highly convincing manner.
The trappings – celebrity endorsements including Luis Figo and José Mourinho, a glossy manifesto, the requisite reform proposals, a convincing manner – were all present and correct.
Manager Arsène Wenger's team bounced back from a home defeat against Aston Villa in convincing manner, exerting control most of the time at Craven Cottage.
Ernie Isley, who has an engagingly sincere, quietly convincing manner, suggested some of the reasons for the continuing success of the act in a conversation that also took in the various phases the Isley Brothers have been through.
A good deal of the respect for the Knicks was engendered by the convincing manner in which they handled the talented Bucks in the first two games of the series.
That may change with research from Facebook that replaces closed eyes with open ones in a remarkably convincing manner.
We do so in a barely convincing manner today, but made an attempt and hope that our efforts serve useful purposes, especially introducing this topic to a broad audience of microbiologists".
That was enough to convince Pope Paul VI to say in 1968 that Peter's bones had been identified "in a convincing manner".
However, little work has been done in visualizing dense foams in a convincing manner.
Mr. Fortuyn managed to express all these views in a clear and convincing manner.
