As far as I can tell, no. There might be something obscure somewhere - in fact I'd be surprised if there was not - but there was no reason to make such regulations. Sex for non-procreative purposes was sinful, period. Pleasure gained from sex was to be kept to a minimum because, while procreation was necessary, one must not delight in the flesh. These rules transcended any petty regulations on specific positions, and made them superfluous.

Late edit:

I'm sorry for the delayed response; I was in transit from a conference yesterday and in meetings all day today.

So there's been numerous objections raised here, all of which seem to concern penitentials. Penitentials do not constitute church doctrine, but rather its practical applications. I have not found any references to such prohibitions (aside from the late 12th c. prohibition on sodomy) in any papal or conciliar decrees. Edicts from these two forms of authority are usually what is meant by "the Catholic Church having rules".

As /u/C1cer0 says below,

The problem is in saying that that the Catholic Church as a whole had a policy on sexual positions in the Middle Ages. We don't have that. What we DO have are penitential manuals--these are books designed for priests handling confession to specify appropriate penance (fasting and such) for various sins. They have the authority of whoever wrote them, and so are more advice books or manuals for running a parish than authoritative church doctrine straight from the Pope.

Here are some sources for further treatment of ecclesiastic opinions sexuality in the Middle Ages. I admit I'm citing around the subject a bit; since there's no papal or conciliar decrees that I have found on the subject, it's an argument from absence, and thus there is no direct citation that I know of.

• Brown, Peter Robert Lamont. The Body and Society: Men, Women, and Sexual Renunciation in Early Christianity. Columbia Classics in Religion. New York: Columbia University Press, 2008.

• Blamires, Alcuin, ed. Woman Defamed and Woman Defended: An Anthology of Medieval Texts. Oxford: Oxford University Press, 1992.

• Makowski, Elizabeth M, and Church Catholic. Canon Law and Cloistered Women: Periculoso and Its Commentators, 1298-1545. Studies in Medieval and Early Modern Canon Law, v. 5. Washington: Catholic University of America Press, 1997.

• Bynum, Caroline Walker. Christian Materiality: An Essay on Religion in Late Medieval Europe. New York : Cambridge, Mass: Zone Books ; Distributed by the MIT Press, 2011.

• ———. Holy Feast and Holy Fast: The Religious Significance of Food to Medieval Women. The New Historicism : Studies in Cultural Poetics. Berkeley: University of California Press, 1987.

• Gregg, Joan Young. Devils, Women, and Jews: Reflections of the Other in Medieval Sermon Stories. SUNY Series in Medieval Studies. Albany: State University of New York Press, 1997.

One of the major issues with this question is that the Church isn't quite so unified as it comes across in this question. There are many bodies within the Church, wespecially in the Middle Ages that pass pronouncements on moral issues. Local councils of bishops, large councils, even individual priests or monks all had authority to make moral pronouncements for their jurisdictions. They could make a pronouncement on anything the papacy did not already cover. This means that when you talk about rules in Catholicism you have to make sure not to lump the entire continent together. Christianity had a different flair in Ireland than it did in Italy.

To get closer to your question: there are several penitentials that have quite a lot to say about sex: when to have it, how to do it, why to have it. These aren't rules, they are meant to help a priest to know what is and isn't a sin when he heard confession and to mete out a good penance. A lot of people automatically claim that these books had a lot more authority than they really did. Most higher-ups disliked them. This post has a good quote from one of these books as well as the flowchart one historian made based on the advice from penitentials.

According to Peter Gardella, there was a belief in the Middle Ages that face-to-face, man on top sex was the only allowable position because other positions were thought to have a contraceptive effect. He doesn't explicitly state it as official church doctrine, but it seems that if that was a popular belief at the time, many church officials would have condemned any other position.

Peter Gardella, Innocent ecstasy: How Christianity Gave America an Ethic of Sexual Pleasure (New York: Oxford University Press, 1985), 13.

According to Paul Collins' book Birth of the West, yes! In a list of penances for sexual sins he states "Male masturbation earned ten days' fast on bread and water, as did fornication with an unmarried woman or maidservant. Mutual masturbation earned thirty days. Female masturbation with a dildo incurred a year's penance. Intercourse in a nonmissionary position incurred ten days' fast, although only five days was required if the sinner was drunk."

His source for this is the Bishop of Worms's Decretum. Note that this only covers one priest's view in the late tenth century, they probably varied somewhat over the centuries that are the Middle Ages.

The problem is in saying that that the Catholic Church as a whole had a policy on sexual positions in the Middle Ages. We don't have that. What we DO have are penitential manuals--these are books designed for priests handling confession to specify appropriate penance (fasting and such) for various sins. They have the authority of whoever wrote them, and so are more advice books or manuals for running a parish than authoritative church doctrine straight from the Pope.

Many don't say anything about sexual positions, though they do talk plenty about adultery, sodomy, incest, times to avoid intercourse, breaking of vows of celibacy, and so on.

But at least some manuals could be read as forbidding certain sexual positions. If you go to http://www.anglo-saxon.net/penance/BX8558_152a.html at the bottom of that page and the top of the next, you'll see the Old English text of a couple of passages from the Canons of Theodore specifying 40 days fasting for someone who "fornicates with his wife from the rear, he must fast for 40 days."

Now you might say that's a prohibition of anal sex. Maybe, but the same document says ejaculation in the mouth is the "worst evil," and the 40 days referred to here is REALLY mild penance by medieval standards, so I think it's not referring to anal sex.

You can click on the red numbers to get modern English translations.

I just wrote a term paper on deformity in the middle ages. Here is probably the most relevant information I found:

Albertus Magnus’ popular work De secretis mulierum’s provides three explanations for why defective children are born: if the woman moved during intercourse; if the woman’s thoughts wandered during intercourse, “for example [if she thought of] a cow, the child might turn out to resemble one”; and if the parents conceived in any non-standard coital position.

Now Albertus Magnus was a Catholic saint but does he speak for the entire church? No… but no one really spoke for the entire church during this period. As others have pointed out, Christianity is never as unified as outsiders perceive. The popularity of Magnus' work is how we judge his influence.

If you're really interested in this topic, you may want to read James Brundage's Law, Sex, and Christian Society in Medieval Europe (University of Chicago Press, 1990). It also includes this completely awesome flowchart which somehow made its way onto Buzzfeed.