I’m not sure what you mean by conflict. There are no characters to have conflict, so I’m assuming that the conflict is with readers and expectations. In his sonnet, (13) "My Mistresses Eyes are Nothing Like the Sun," appears to be a poem that is insulting. The narrator notes all of these beautiful things like sun, snow, roses, perfume, music, and etc. As he is noting them, he compares them to his mistress whom we are clearly told does not measure up to any of these things. Even though he appears to speaking badly of his mistress he ends the poem by telling us, in a sense, "It doesn’t matter if she doesn’t meet your expectations of what is beautiful, I see who she is inside and out, and she is beautiful to me." As relationships grow and mature, the initial superficial aspects such become deeper and more meaningful. Clearly the speaker has realized his love for the mistress is based on deeper and more meaningful things. She’s not attractive maybe by societal standards, but it can be compared to the idea in Pope’s "The Rape of the Lock" that when beauty fades there better be intelligence, good character, and etc.
I agree with the previous poster and want to add that the conflict in Sonnet 130 can also be viewed in terms of the poet's challenge to well established poetic ideals of female beauty. These older ideals are usually identified as "Petrarchan" and include, among other things, the sense that the woman is distant and perhaps even cold and heartless, even to the point of using beautful but hard/cold terms to describe her features, such as snow, gold, coral, and rubies.