To make Muiri eligible to become a marriage candidate you need to complete the Dark Brotherhood quest Mourning Never Comes.

I just finished that quest, but in an indirect way. Apparently I already killed Alain Dufont earlier in the game. The quest is still completable but you don't get the chance to kill the secondary target. I don't know if some time has to pass for her to become a candidate, but literally right after she paid me I checked but never saw an "interest" option. I haven't even spoke to Astrid yet. To be able to marry Muiri, does the quest have to be completed the correct way without having Dufont dead prior to starting the quest?

It's necessary to get the quest first, otherwise the secondary target doesn't become an option.

That svcks, because it looks like with having killed Alain Dufont prior to the quest renders the secondary target unnecessary and therefore unkillable. Thusly making Muiri unmarriable...

Yep, sorry - didn't word that very well