The phrase "almost convinced" is correct and can be used in written English.
You can use it to describe a situation in which someone is close to being fully convinced of something. For example: "I was almost convinced that I needed to get a new car, but then I was able to get my old one repaired instead."
My luck was changing, and I was almost convinced I would find Fumiko waiting for me at my door.
The source said Lula, Rousseff's predecessor and political mentor, was almost convinced he should take the position.
I was almost convinced, but then his cogent analysis veered abruptly toward conjecture: "Traditional Russian cold beverages, like kvass and mors," he continued, "also do not require ice".
By the time I had polished off a second helping proffered by our genially patrician host, I had almost convinced myself that I was eating mutton.
It sounds stupid, but he's so good at convincing them, my mother and I laugh and tell each other, "He's almost convinced us".
I had almost convinced myself that I hadn't missed out on much, that it couldn't have been that fun, that having cats was basically the same thing... when the twins decided to go in for a second round.
Their indie rock, psychedelic pop, dance, country, glam and space-folk mashup was as pioneering as their aesthetic was madcap – they sang witty songs about unicorns and alien abductions, toured festivals in an army tank, filled stages with yetis and milk floats, and almost convinced Creation Records to buy them an aircraft carrier, which they'd planned to turn into a nightclub.
Of course I now routinely refer to it as "my" film and have almost convinced myself that I not only wrote it but produced and directed it - but anyway huge thanks to Nick Hornby, Amanda Posey, Finola Dwyer, and Lone Scherfig for making such a good job of it.
"I am almost convinced of it," he responded.
I have read heaps of agricultural & horticultural books, & have never ceased collecting facts At last gleams of light have come, & I am almost convinced (quite contrary to opinion I started with) that species are not (it is like confessing a murder) immutable.
"I am almost convinced of it," Lebed responded.
