Is one halachicly allowed to set up two non-Jews for marriage? I don't see why it should be an issue,but not sure. I wondered if anyone discusses this.
Rabbi Tuvya Golstein gave a shiur about this. See in the seffer Emek Halacha, which was collated from tapes of the shiurim and his students writings, siman #46.
He quotes a machlokes achronim about this matter who base their opinions on rishonim. Basically it all hinges on whether nochrim have a mitzvah of pru urvu, having children. He touches on many points of that discussion and different opinions between helping birth them or helping them conceive, for free or with a fee, and of course, eiva (which always makes answering a question like this in a pubplic forum strange).
The stringent opinion is the Chavos Yair #185 who says:
There is no issur [to arrange their marriage] as Ramban allowed healing a nochris to be able to give birth as brought in Rashba 150. However I have a tradition from gedolim that one who involved himself with this is not free from 'burning his food'.
Rabbi Golstein adds that his words are brought in Ba'er Heitev Yoreh Deah 1:15.
On the lenient side of this discussion is Mahari Assad in Yoreh Deah 230:2 who says:
One may arrange a marriage between nochrim. He says this is a kal vichomer from being allowed to heal them in order to have children. Also we find that nochrim are commanded in sheves like a slave (Gitten 41) and see Tosafos Chagiga 2b that pru urvu was said to all bnei noach.
Rabbi Golstein takes extreme issue with this last statement. All the Achronim, Maharsha first and foremost say this is not true as we know from Sanhedrin 59b pru urvu does not apply to nochrim. Mishneh Lamelech Chapter 10 of hilchos milachim halacha 7 says Tosafos were obviously only referring to a Jewish owned slave.
He also brings a list of other achronim, Shvus Yaakov Sfas Emes Emek Shaila who try to reconcile the words of Tosafos, but all obviously hold that nochrim certainly do not have pru urvu.
Considering all this he rules stringently saying we must take the tradition of the Chavos Yair into consideration, and we may not arrange their marriage.
He also adds that he saw in Beis Shearim Yo'D #227 to be stringent. It was a responsum to his own son at the end of which he added that even in a situation of extreme necessity for a livelihood he should be stringent and Hashem will send him sustenance from an allowed source.
Earlier Rabbi Goldstein also mentions the issue of speaking good of a nochri which will obviously come up when mentioning each parties virtues to other. This is not allowed as per Rambam chapter 10 hilchos A.Z. Chinuch 426 # Yoreh Deah 151:14.
Every man should marry a woman, and every woman should marry a man since it is written “that it is not good for a man to live alone by himself.” Marriage brings about a partnership between two people and increases the population of the world. In marriage a Noahide will participate and contribute in the building of the world. Marriage is initiated by the couple’s decision to live together as husband and wife followed by their sexual union.
All of humanity has been commanded to “be fruitful and multiply,” and therefore it is important to have some rituals to follow with respect to marriage (of Noachides).
Therefore it seems that it is, in principle, good to facilitate the marriage of non-Jews within the structure of the laws of the Noachides.