Nathan Hopson writes from a conference at Nagoya, Japan:
Since these are neologisms, there are no established English translations for either of the terms. Consequently, instead of offering translations for these terms, I will try to explain what they mean, and then invite Language Log readers to suggest their own translations.
We may think of tóngqī 同妻 as an abbreviation for tóngxìngliàn zhàngfū de qīzi 同性恋丈夫的妻子 ("a wife who has a gay / homosexual husband") and tóngfū 同夫 might be thought of as an abbreviation for tóngxìngliàn qīzi de zhàngfū 同性恋妻子的丈夫 ("a husband who has a lesbian / homosexual wife").
This may sound very odd to American readers, but the general context for these terms is that Chinese law doesn't permit same sex marriage. Consequently, a gay man, under external pressure (mainly from family) to marry, will enter into a tóngqī 同妻 arrangement with a woman who is willing to accommodate him, and vice versa for a tóngfū 同夫.
[Thanks to Fangyi Cheng and Yixue Yang]