Hmmm... хрошечка (KHRO-shetch-ka, with the KH sounding something like the Hebrew CH in l'chayim or the Spanish J in jalapeño) is a traditional Russian term of endearment -- there's even a fairytale about a Cinderella-like heroine who's nicknamed "Khroshechka". Literally, it means "Wee little crumb," and has nothing to do with birds. So if the girl's Russian boyfriend knew English pretty well, he might possibly invent the Anglo-Russian portmanteau "Crow-shechka" -- signifying "a cute little thing who is also dark, mysterious, and intelligent."
Another possibility: Maybe the boyfriend could use a "typical and natural sounding" Russian term of endearment when he's in a cuddly mood (maybe "Lapushka," pronounced LA-poosh-ka, which literally signifies something like "My little puppy-paw"). But if he wants to tease her, he could use something slightly unflattering, like "Voronyonok" (vo-ro-ÑO-nok, with the Ñ as in Spanish "señor"), meaning "Baby raven."