One trick we're using is that the order is always random, and whoever's turn it is gets to pick who is next. Ideally you pick the one who is not paying attention.
If enough people are having trouble paying attention that it's becoming a problem, your standups suck. Your team may not need them (they may be communicating just fine without them) or may need them to be run differently. You may have too many people in them, implicit or explicit expectations of saying stuff just to have something to say (which contributes to people losing interest and tuning out), you may have multiple barely- or not-at-all connected teams in the same standup (I've seen this! And of course every member of one team tunes completely out when someone from another team is talking) or any number of other problems. Or, again, your team may just not need daily standups because they communicate fine without them.