I'm not sure which source you used for conciliate, but the word does not mean a "falling out". The word conciliate means: Gaining trust/favor Overcome distrust Make things right Some synonyms would be: appease pacify satisfy Some antonyms would be incite irritate instigate a fight The word used in common speech to describe conciliation between couples is "make up" Example: In the marital life, sometimes couples can't get along with each other for a few days. After that, they make up. Hope this helps :)

You can say, "they had a brief falling out, but then they reconciled." Reconcile (not concile) is the word and it's fine to use in any situation. You could also say, "they had a spat", which is a small fight, or even "they had a fight that kept them apart for a few days." If you mean "they went to councilor".