How to get Leviathans to stay

I've had the Leviathans come by a few times and I keep clicking feed elders, and they are always displeased and leave. Is there a certain way to get them to stay? or are the chances of them staying random?

Ahh, kittens game. A long time ago...

Anyhow, the faq states that:

NOTE: You may feed the elders with a sacrifice. If they're pleased, they will stay. If not, they'll just leave.

That will get you nowhere, as you already tried that. So looking into the source code is the next step in unravelling this mystery. It seems to be in the diplomacy tab, and this is the specific code about obtaining Leviathans:

var ncorns = this.game.resPool.get("necrocorn");
elders = this.game.diplomacy.get("leviathans");
if (ncorns.value > 0){
    elders.energy += ncorns.value;
    ncorns.value = 0;
    this.game.msg("Elder gods are pleased", "notice");
} else {
    this.game.msg("Elder gods are displeased", "notice");
    elders.duration = 0;
}

I haven't played in a long while, so I am unfamiliar with the necrocorns or how to obtain them. In the faq it says that you'll get them from the Marker building in the religion tab.

Effects: Starts a ticking corruption countdown that slowly changes alicorns into necrocorns

However, it seems that when you have more then 0 of that (so any), you will get your precious Leviathans.

TLDR. Build a Marker building in the religion tab. Obtain Necrocorns. Feed Elders. Obtain Leviathans. Profit.