Here's some paradigmatic info on just what determines the sex of a child. My source is Thomas Lacquer's Making Sex: Body and Gender from the Greeks to Freud, p. 39.
It appears that sex is determined by a combat between male and female sperm in the uterus (or so the Hippocratic tradition asserts--I am unable to find anything in Lacquer's book that describes how sex is determined in the Galenic and Aristotelian systems). Should both partners produce strong sperm, a male child is the result; should both produce weak sperm, a female child is born. If one partner contributes weak sperm and the other strong, then it is quantity that determines the sex of the child (i.e., a large amount of weak sperm, whether from the male or the female, can overwhelm a smaller amount of strong sperm, no matter what its source). So the Hippocratic model involves a battle or struggle for supremacy, generating a fluid situation in which the power of the seed is independent from the parent generating it.
Galen's model depends more on an economy of heat (the male seed is hotter and drier than the cold and wet female seed), while Aristotle's denies that any blending of mixture takes places, that the superior male sperm molds and shapes the weak and formless female seed into a child. As I said above, Lacquer's book doesn't explain how determination of sex takes place in these systems, but I can offer these two hypotheses. (1) Galenic - certain environmental conditions can alter sperm temperature, so it's possible that a man who, through some chain of events or diet or lifestyle, has colder sperm will only be able to beget girl children. (2) Aristotelian - again, something external causes the male's sperm to exercise a weaker sculpting, forming effect.
So whatever ritual one comes up with is going to have to make sure that the man's sperm is strong, hot, and ready to shape that which is shapeless. Maybe a ReCo with an Ig requisite? Have the Duke do all sorts of embarrassing preparatory exercises; after all, it's mostly his fault that he's not getting male children upon his wife. Have him sit in a hot bath, eat hot and spicy foods, engage in manly activities, etc. Whatever you do, don't have the wife engage in any of these things--bad things could happen if the wife became "hot" in terms of her temperature (for example, in one spectacular and paradigmatic example, a young woman running at top speed through a field grew overheated, jumped a fence, and underwent a sex change in mid-air; since much of paradigm believed in a one sex model, the heat caused her normally cold genitalia to descend outside her body and become their external male analogs).
And remember, whatever happens, the Duke still needs to bed his wife, and both partners must have an orgasm. No mutual orgasm in the Middle Ages, no child.
Rob