"my earnest" is not a correct and usable phrase in written English.
To use an earnest phrase in written English, you would need to use the phrase "in earnest," as in "I began the project in earnest."
She wrote in her journal, "my earnest desire is to compose a course of teaching for Charity Schools, by which the children may learn in reality, and not by rote, the principles of the Christian Religion, as taught in the Scriptures".
Nor have Mr. Colbert's people replied to my earnest entreaties.
Plenty of my earnest broadsheet journalist chums agree (on balance).
And I harangue those people, I bore them with my earnest insistence.
Her response to my earnest proposal of marriage was "Ti Durak!" (You're an idiot!).
No doubt my earnest reports from Port of Spain and Madras suggested cricket would never be the same again.
I saw my Earnest-O-Meter explode and frighten my dogs.
But my standing, thanks to my modest prosperity and education, means that I shall have to humor Barney, and no doubt my most earnest cautions about the forty-year age gap between Barney and my mother will be flung back in my face, Szabo thought.
According to my peppy, earnest, and serious trainer, I must "recover"—by pumping my legs away on the cardio machine for three to five minutes.
When I made my first earnest step toward what would eventually turn into changing my career, I was just doing something that filled me up--writing--because I couldn't stand to not do it any longer.
(And by my own earnest assertion, under-appreciated national treasure).
