The premise of this is kind of crack, but I am taking it more or less seriously. When Janeway turns Q down, Q goes to Picard and takes female form to get Picard to be the father of her child.
Plan B: Janeway explains why Q asking her to bear his child is offensive. Q comes up with a different plan.
War Stories: Incomplete. Q comes to Picard, bereaved by the sudden loss of his companion and best friend, to ask him to help Q in a plan to stop the war in the Continuum. From Picard's perspective, it is an incredibly weird plan, but Q doesn't see what's wrong with it. P/Q, genderswap.
Seventeen Things That Might Have Happened To Q, Chp. 15, "Knitting": One of the seventeen AU's from "Seventeen Things That Might Have Happened To Q" belongs to this series. Q is knitting a baby.
A Doctor, A Q and a Baby: This is P/C and P/Q, genderswap. A human baby needs a human mother. Beverly Crusher and Q fight over Picard and the proper care of Q babies. P/C, P/Q, Q in female form.