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Since I read Old Japanese only had open syllables, what does the Modern syllabic /N/ derive from? Any examples?

It was first imported from Chinese, along with diphthongs and geminate consonants, and later ones popped up from reduction of syllables with nasal or voiced labial consonants (Onbin)

The board hates non-ASCII characters in the URL: https://en.wikipedia.org/wiki/Japanese_ ... _changes_(音便_onbin)

Japanese

A simple example would be 天. It was pronounced something like /tʰen/ or /tʰien/ in Middle Chinese and would've been borrowed into Old Japanese most likely with the pronunciation /tʲeN/ (compare Vietnamese thiên and Korean cheon), which eventually became /teN/ by Middle Japanese.

Internally, Japanese itself saw many nasal-vowel syllables (typically with a high vowel) reduce to a moraic nasal by either Early Middle Japanese or Late Middle Japanese. A classical example is how /jomi-/ "read" + /-te/ became /joNde/ 読んで. There are also limited examples of /N/ originating from voiced labial consonants, e.g. /tobi-/ "fly" + /-te/ became /toNde/ 飛んで.

Still an active process dialectally

The process of nasal-vowel syllable reduction is still active in some dialects. For example, in the Kagoshima dialect, it's so pervasive that nearly all /ni/, /nu/, /mi/ and /mu/ syllables have become /N/. For example, /kamu/ "to bite" and /kami/ "hair" are both /kaN/ in this dialect.

Ryukyuan

And just in case you're curious, all Ryukyuan varieties also have /N/ both in borrowed Chinese words and in native words and verbs, so it's certain that the sound change started before the Ryukyuan varieties split off from mainland Japanese.

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Chances are it's Ryukyuan (Resources).