Hi Mimsey,the correct spelling in Serbo-Croatian is: "tamburica" in Latin fonts; if written in Cyrillic fonts, the scientific transliteration is the same. Since in most West European the letter C- is pronounced as a K- before -a, -o and -u, it is transscribed as -ts and -tz according to the preferences of writing in the intaking language. The -OU- is clearly French, because the letter U is pronounced like Ü (U-Umlaut, a sound special to German, Scandinavian languages, and Turkish). "Tambourtsa" and "tambor-" which Wolfgang gives also seem to me like misspellings with letter omitted due to hurry or misunderstanding.
Enjoy the sound! Wilfried