The phrase "generally convincing" is correct and can be used in written English.
You would use the phrase when you are trying to emphasize the level of convincingness a particular argument, statement, or idea has. For example: "The data was generally convincing, but there were a few questionable points that needed further exploration".
Mr. Krishna's ideas for alleviating poverty are generally convincing.
Each critique is simply a few stock phrases strung together, but it is generally convincing unless a judge's remarks seem contradictory or one judge blasts you and then the next judge says "I totally disagree" and also blasts you.
If David Brooks is seriously concerned about the increasing polarization of the country, he might advise the leaders of the Republican Party to cease equating liberals with wooly-headed spendthrifts and generally convincing rank-and-file Republicans that those who criticize Bush administration policies do so because they hate America.
Already during the summer 2011 debt crisis, Jeffrey Rosen wrote a generally convincing piece arguing that invoking the Fourteenth Amendment was valid and would likely be upheld by the Supreme Court.
Petit said that, in spite of generally convincing non-player character design, "character models look like plastic dolls when viewed up close, and some gestures characters make are rigid and unnatural".
There are more than 100 pages of invented – and generally convincing – journal extracts.
In Ireland, Croatia, Latvia, Greece and Iceland rates rose by over 50%.I should say at the outset that I am generally convinced by what I've read in this report.
Insiders, however, are generally convinced that what we do now matters tremendously, because the difference between the best- and worst-case scenarios is vast, and the future is not yet written.
He went on believing that we were shockable well after he had ceased to shock us (John Waters has the same problem), and most viewers of the last Almodóvar picture, "Kika," were generally convinced that they were staring at a dead end.
But the larger part of the rise in G.E.'s stock price reflects the fact that investors were very suspicious of stocks as investments in 1981 and by this year were generally convinced the stock market was sure to be the best long-term investment.
Those results generally convinced physicists that Einstein was wrong.
