Some of you might think that should be the manager's job and not mine, and the manager should have dealt with this already but that's not the situation I am in. I have to and I want to take responsibility and resolve this conflict.
This is a good responsibility to take up and prove that you have managerial skills apart from technical ones. Just be careful not to rub people the wrong way, or to lose your technical skills in the process.
Some of the tasks assigned to me is to ensure that the project is executed successfully, review all technical aspects of the project, set clear boundaries between the two developers so that they don't step on each others' toes, and ensure that they don't get into any more conflicts.
There are many ways to approach such a situation. A lot of this depends on your personality. The general strategy I would employ would be give subtle, verbal and non-verbal signals that fighting is not appreciated among the team. This would include letting the people concerned know that it would impact their appraisal negatively -again hints rather than threats.
You should be able to carry this off for it to not backfire.
Most of these conflicts began before I joined the team but now that I am here, I want to minimize conflicts between them and resolve them amicably.
One way to look at these conflicts is to pretend (takes time and effort) that they are merely technical problems rather than the personal, ego-based issues that they are. Assuming you have the time or can take some out, call get everyone's inputs, and tell them you will take a decision based on the respective merits of the library.
Option A:
If having two libraries is not a maintenance issue (the code does not give you too much trouble) simply let both lie and tell both people concerned there are many more important things to do - discuss pending Quadrant II deadlines here. Get them involved in those.
Option B:
Let both people that you are looking at cross-domain skills, and you will decide on a library - but the person who has earlier worked on the library will not be the one doing the implementation, the other person will.
This is slightly nasty, but should tempers cooled down pretty fast.
For the long run, create the impression that you do not want to discuss specifics, are not interested in personal arguments - but do want to help the person grow as a whole. They will eventually stop complaining.
In general, never literally get into a fight between two subordinates and take sides - as in when it is actually happening.