How did Song of Songs, which is mostly a collection of love poetry, enter into the Biblical canon - and how did early church fathers justify its inclusion?

Well, canonization of the Bible is interesting and hard subject. One of the reasons why it is hard is that canon depends on who you ask. Catholic, Protestant, Orthodox and Jewish perspective is different on that what is a canon, and what isn't. I assume that your question is about canon present in Vulgate, the translation of Jerome. So my short answer will be directed to that canon. For better understanding i listed in sources books that can help you.

The books, which belong to Old Testament, are collected by the Jewish priests Ezra and Nehemiah, In fifth century B.C. As such this collection was later translated into Septuagint (Greek translation of Old Testament) and translation of these texts were used for Vulgate, with some minor changes. Why? One explanation is that, these texts were oldest accessible for them at the time (any time actually), main topic of that texts were connection between God and man and it contained prophecy about Messiah. Some Hebrew writing were excluded and marked as apocryph, because they portrayed someone else as Messiah and not Jesus or they had nothing to do with God.

This book, the Song of Songs, was present in Septuagint, in Ezra and Nehemiah collection and it was listed by Flavius Josephus as holy book. So it was hard to exclude it from canon.

How did early church fathers justify its inclusion?This is good question. The subject of the Song of Songs (or highest Song) is love and sexual longing between man and women, Solomon and Shulamit. So it has nothing to do with God, directly. That's why christian fathers looked for allegory. Their interpretation shifted over the centuries. But they usually are treating the love, between man and woman, as an analogy for the love between God and Church or Jesus and Church (Church like community, not the building). Today there are even more interpretations of the songs.

Sources:

-Encyclopaedia Judaica, 1973, fourth volume - Here you can find a lot of information about collection of Old Testament's books.

-Flavius Josephus, Against Apion (I, 38-41 [8]) - Flavius Josephus lists the books who Jewish consider holy. And book generally is about religion and philosophy of Jews.

-Norris, Richard Alfred 2003, The Song of Songs: Interpreted by Early Christian and Medieval Commentators - Here you can find early Christian interpretation of song.