He may want to marry her for her money, and not for love. Mr. Elton gives Emma a poem seemingly intended for Harriet, which when its riddle is deciphered seems to be a love poem to Harriet. This convinces Emma of Mr. Elton's intentions toward Harriet. Emma continues to advise Harriet Smith on romantic matters, telling her to not betray her feelings to Mr. Elton. The poem he writes is intended for Harriet Smith's collection, yet he shows it to Emma.
Manners provide some obstacle to resolving the situation.
Since nothing can be openly declared, both Emma and Harriet must rely on the subtle clues that Mr. Elton gives. He can write a private riddle with the solution 'courtship,' but he cannot discuss the actual topic with either woman. Games and riddles dominate this chapter of the novel, apt metaphors for Mr. Elton's courtship tactics. And in this situation Mr. Elton is deliberately engaged in a charade. He now seems quite aware of Emma's intentions and plays along with them to remain close to Emma.