I'm fairly certain the Coptic Church is officially opposed to it; I have a booklet by HH Pope Shenouda of most blessed memory, that condemns it with abortion and homosexuality if memory serves...ai would have to dig it out. It was part of the impressive set he compiled on faith, morals and theology, of which On Calmness is my favorite.
While I am not sure that I am absolutely opposed to birth control as a means of timing the birth of children and allowing marital relations to resume which might perhaps allow the wife a chance to recover more fully between pregnancies, in order to increase the likelihood of success on the next pregnancy (assuming birth control actually does that; I think some forms of it like IUDs might well have the opposite effect and traumatized the uterus, decreasing the likelihood of a successful pregnancy further on, I think the use of it to limit the size of a family as abhorrent. Particularly in the case of the Oriental Orthodox, who are facing the real prospect of attempted genocide even in Egypt, and whose numbers are low everywhere except Ethiopia. In particular, a high birth rate for critically endangered Suroye populations I think is warranted. But I wish there were 60 million Armenians and not 10 or so, and for that matter, as many Copts as Muslims in Egypt, and tens of millions of Suroye, and for that matter Assyrians, and Syriac, Chaldean and Maronite Catholics, enough population to make a dent in the Islamic hegemony. And millions more Nasranis, so that Christians might go from being the third largest religion in India to the second or even the first.
And happily towards that end I'm pleased to report the local Syriac and Coptic parishes are full of children and youth. And I love the way I see parents here in the diaspora treating their children. It's beautiful to see the families existing in such a state of love, so happy and excited, in the social hall, after liturgy. And birth control would turn those social halls into empty, tomb like places. Which is why I think the Pope is spot on in just outright banning birth control, that all of his parishes might ring with the laughter of children in the warm glow that follows the Eucharistic banquet.
I really wish Alexandra read this forum so she could see this post, I might link her.