Really, any member of the Lute family is a cousin to the mandolin. That is any hollow bodied fretted stringed instrument including guitars and citterns. The Lute itself is a descendent of the Lyre going back a long time, being a multi-stringed instrument with the strings running over the soundboard. A neck and tuning pegs and a pear-shaped body make it distinctive as a different instrument from the Lyre. The Arabic Oud or Ud is probably the proto-lute.
The other members of the family make up an assortment of instruments which evolved as the Lute spread along trade routes in Europe and Asia.
All the following are of the Lute family and therefore cousins to the mandolin: Guitar, Ukulele, Sitar, Bouzouki, Tanbour, Oud, Saz, Banjo (yes banjo!), Pipa, Liuqin, Sanxian, Rabab, Cittern, Balalaika.
By no means a definitive list.
The closer relatives such as the guitar and bouzouki have found a place in folk and English / Irish traditional music.
Since the Modern 4-course Greek Bouzouki was adapted in the 60's for Irish tunes, there has been a growth in the number of instruments which can loosely be described as:
"Longer than a mandolin and deeper in pitch, with 4 or more courses"
At the end of the day of course, it doesn't matter at all - playing is what counts with whatever instrument you're happy with. Here are a few of the commoner relatives for comparison:
|Traditional Greek Bouzouki||DAD||660mm|
|Modern Greek Bouzouki||CFAD||660mm|
DGBE (chicago - guitar)
The Tuning is given as Low to High (Thickest, deepest sounding to Thinnest, highest sounding)