I use decks of cards–you can pair by color, suit, number, etc. Plus if you have an uneven number of students I throw in a Joker card and whatever student draws the Joker gets to join the group of his or her choice.
In the past I’ve handed out clocks printed out on paper and the students got to fill in students for each hour, then I’d have them work with their “2 o’clock” partner on some days and “7 o’clock” partner on others, etc…