I'll do that too. Basically I will attack and capture/destroy several of their cities, then I will extort money or technology out of them. I would only do this to one civilization at a time though, if you tick off too many civilizations they tend to band together and go after you... and it can be difficult fighting three fronts at once
Tell me about it! Only I wasn't the ticker-offer--they jumped on me unprovoked

there I was, peaceably finishing off the Aztecs when Xerxs sends a cav, a longbow, and a sword into my newly conq--assimilated lands. He says he's just visiting, but I notice there's nothing to visit except me & sure enough he declares the next turn around. Now, I've just gotten my first 2 armies, so I finish off the last 'tecs & hustle them over to the other side to confront Xerxs. I get a little worried about William watching all this from the sidelines, so I invite him to the party & we proceed to make Xerxs do the Big Dance. Now--I don't really want to conq--assimilate Persia at this point; I'm not ready yet. So I send my now-4 armies off on a little sightseeing tour of the Persian heartland. I'm afraid they're a little messy, though; landscape just doesn't seem the same where they've been. Meanwhile, Willie gets tired, goes home--and next thing I see is Izzie's cavalry riding in from the north, thru Willie's demesne &, uh-huh, you guessed it: she declares next turn. I make nice with Xerxs, having glommed a stray silk he no longer needed & a lonely saltpeter that I sure did, & get the armies busy healing, because--yep--Willie joins Izzie & now I've got a maximal front to defend & not all that many bodies to do it with.
And about the time I locate Izzie's longbow rush SOD--hilarious, but with enough bodies you can grind down any stone in time--Osman decides to drop a few warriors on one of my offshore islands, just to give my swordsman & dromons a workout. . . .
Latest is that I've roped the Portuguese & Indians in on my side, just to be able to keep track of them, I sold Xerxs on steam, so I could soak up his unnecessary cash to use for upgrading my cannons. . . and the Portuguese cavalry & navy seem to be lining up next to the dyes I've got on another offshore holding. If WWI wasn't enough, I smell a sellout in the making
I'm estimating I'll just be able to steal some wine from Willie (& take his capital) right about the time the Ports get dyed, but won't really be able to finish him off. Yet
My one edge: 6 4-strong cav armies, & rails deluxe. And a goodly number of frigates & dromons acting in concert. I'm a peaceable kind of guy, but these AI's are gonna get seriously talked to the only way they'll listen, & the conversation promises to get just a mite, um, energetic
kk