Maybe the influence shouldn't decrease at all. We just couldn't buy it.
Purchasing food, culture and units would be a different thing. Of course a friendly CS would propose better deals for them, and an allied one even better. So befriending them would be important even if diplo victory is off.
For culture it would be: "we sent some of our greatest artists at your court for a while", etc... If we don't need the bonus that much we keep our gold but the influence remains.
Quests and active protection would be everything. As it's been said:
it makes more sense that City States vote for whoever is willing to look out for the City States best interests (their current allies).
Pledging to protect (PtP) would make influence increase slowly with time. But we would have to be careful cause letting one down when attacked would hardly be forgiven and badly affect relations with other CSs who wouldn't take our pledges for much any more. Asking for a 10 turns delay would be the maximum, later only a liberation could make them forgive, and not at all like if you had declared war on time. Every enemy unit you kill would count a little, especially close to their city. You could give an "ultimatum" (is that english?) to a civ who attacks a CS your PtP ("let them alone or we're at war"). If they refuse war is auto-declared. If they accept (maybe they just wanted to test you) your influence of course grows even if you didn't fight.
Also if you can manage peace for a CS you didn't pledged anything. Can be safer if they happen to sit at the other end of Mother Russia.
The current system is a bit confusing, I'd like a clear symbol like a shield that we could see from the main view on the CSs we PtP. Entering their screen, we could see other shields if other civs did the same. Also maybe the level of influence of other civs could appear on the bar. This could be a single bar divided in 3 parts neutral-friendly-allied (if positive..) so others civs could appear on it even if just friends. (By the way... maybe their screens could be more unique and colorful. They have different musics, wich is good, why not different screens with buildings or any stuff of their own style? I imagine Venice, etc.. It could give them just a little more substance)
And as it's been said barb camps could always matter (they just could make a universal call), and the strength of gifted units too. Maybe gold could still buy influence but at crazy price and disconnected from purchase of food, etc...
When a CS asks you to destroy another one you befriend, you could pay them to bury the dispute so they propose another quest and remove the target from the head of your protected.
Tu put some oil on the fire, the capture of a CS could bring a lot of gold.
Sorry I was a bit long with unperfect english but I love CSs, I think they really are a great add to the game with a lot of potential.