There's virtually no reason not to invest in city-states regardless of which civ you are... but nonetheless it's a fine question. I think the first obvious suggestion would be to farm river-side tiles as Civil service makes them quite good for growth and will allow you to run other food deficit tiles.
Something I liked to do is to farm riverside hills, as it produces 2f 2p 1g with civil service, making it a nice well-rounded tile for a city.