キミを忘れないよ by 大原櫻子
"kimi wo wasurenai yo" by Sakurako Ohara
both your song title and lyric seem to include furigana for the katakana and kanji, which amounts to repeating things.
The line you're asking about is キミの涙がこぼれ落ちないように, as in 零れる＋落ちる (koboreru + ochiru = koboreochiru), こぼれ落ちる (to spill+fall)
Click on the words above for their dictionary entries.
Full Lyrics here