Yeah, city-states should definitely have trade routes. It'd add to the feeling like they are actual smaller nations that engage in their own affairs instead of existing for the purpose of giving you stuff when thrown money at. ...And honestly the trade routes shouldn't be based on who they like most, they should base it off which one gives them the most gold. They might be a bit more eager to send you stuff if you're their ally, but if your cities suck to send trade routes to, they should go for better cities to trade with even if they don't have relations with those. Or maybe they'll even send trade routes to other city-states.