There is certainly irony in Elizabeth Barrett Browning's sonnet cycle Sonnets from the Portuguese. In fact, there is a deep irony that underlies the cycle as a whole. Browning wrote these poems for her husband, and in them, she marvels over the irony that he would fall in love with someone like her, someone so frail and sickly. Yet despite all appearances and all expectations, their love is real, and these sonnets express Browning's wonder at that love.
Let's look at some examples of irony in individual sonnets as well. In Sonnet 28, for instance, Browning speaks of the "dead paper" on which she composes her letters. It is "mute and white," yet ironically, it contains an expression of her living love, so much so that the letters themselves "seem alive and quivering."
In Sonnet 9, the poet begins with a question: "Can it be right to give what I can give?" She feels unequal to her beloved and wonders if she will only cause him grief. The gifts she can give him are ungenerous, she believes, and she feels that she will only "soil" his "purple with [her] dust," only bring him down to her level. Yet, ironically, what appears on the surface is only that, an appearance; for their love is real, and therefore, she must let her questions and concerns pass.
Sonnet 24 also contains irony. In this poem, Browning speaks of how the couple's love shelters them from the sharpness of the world. "The lilies of our lives," she says, "may reassure / Their blooms from their roots." Lilies appear to be fragile flowers, ready to wilt and fade at the slightest difficulty, but appearances and reality do not match in the case of what the lilies represent. The lives of the lovers are strengthened by a hidden source, the "heavenly dews" that support their firm, stable roots and allow them to grow straight and tall. Here is the irony; what appears is not truly what is.