Perhaps Harriet’s earnestness is affected by how she suspects her wishes will be received by Emma. Harriet may be as earnest as she feels in wishing to be nursed by Mrs. Goddard for there is no reason to suppose it will garner Emma’s disapproval but the same cannot be said of a proposal from Mr. Martin. Emma has openly disparaged him since their first discussion in Ch. 4 and I think it has taught Harriet to moderate the expression of her feelings about him before Emma:

“…and this letter was from him, from Mr. Martin, and contained a direct proposal of marriage. "Who could have thought it! She was so surprized she did not know what to do. Yes, quite a proposal of marriage; and a very good letter, at least she thought so. And he wrote as if he really loved her very much -- but she did not know -- and so, she was come as fast as she could to ask Miss Woodhouse what she should do." -- Emma was half ashamed of her friend for seeming so pleased and so doubtful." (7)

It seems right to point out honoring Harriet’s wish to be nursed by Mrs. Goddard does not affect Emma’s matchmaking plans. The same cannot be said of Mr. Martin’s proposal so I am not convinced if Harriet had been earnest in wishing to accept him Emma would have honored it. Accepting Robert Martin not only ruins Emma’s plans but I think in her mind would make a mockery of her efforts to improve Harriet. Putting earnestness aside it appears Emma realized Harriet wished to accept Mr. Martin:

"You think I ought to refuse him then," said Harriet, looking down.

"Ought to refuse him! My dear Harriet, what do you mean? Are you in any doubt as to that? I thought -- but I beg your pardon, perhaps I have been under a mistake. I certainly have been misunderstanding you, if you feel in doubt as to the purport of your answer. I had imagined you were consulting me only as to the wording of it."

Harriet was silent. With a little reserve of manner, Emma continued:

"You mean to return a favourable answer, I collect. …I shall not give you any advice, Harriet. I will have nothing to do with it. This is a point which you must settle with your own feelings." (7)

I think Harriet’s continuing admiration and her willingness to accept him despite all Emma has done to drive the “young farmer out of Harriet's head” (4) ought to have caused Emma to at least reassess her plan. It does not, Emma’s conscious is untouched but it is not surprising because when Emma saw Harriet’s admiration for Mr. Martin in her “smiling face” and “flutter of spirits” in Ch. 4 she saw it only as reason to use her influence against him. I don’t know what could have made Emma sensible Harriet’s natural inclinations, opposed to those Emma instills in her, ought to be honored. After Mr. Elton has proved himself “in many respects, the very reverse of what she had meant and believed him” (16) to be Emma still feels persuading Harriet “not to accept young Martin” (16) was the right thing to do.