If you are the principal investigator and notice conflict of interest between two of your coauthors, how would you manage it?
Let the co-authors to discuss it between themselves first. If doesn't help, let them each separately write a letter to you outlining the arguments, and the conflict status. At this point, be ready to resolve the conflict fairly and squarely.
Let me tell you a suggestion. If I were you I would adopt the nominal group technique for them. You should inform them that you realized there is a conflict which block the work and the project is in danger. Asked each of them to find out the way how do she/he can change her/his job to help finishing the project. After that they can give some other aspects to each other what would be welcomed. Of course when you sit them together to discuss the proposals you need a moderator, a mediator is better. You can do it! Good luck!
Conflict of interest suggests that an academic should not be an author.
Conflict between co-authors is a separate issue.
SOP.