The bartender pulls the Cyclops aside and says “You weren’t kidding the other day when you told me you knew a guy who’s hung like a horse!”
Thank you so much! (I only wish I could have come up with some role for the centaur as well…)
OK, I didn’t get it at first, either, but…
Then the bartender says ‘don’t you mean a martini?’
and the Cyclops replies ‘no, those make me double.’
The bartender asks the cyclops, “Why do a centaur and a cyclops make good drinking buddies?”
The cyclops says, “Well, if i drink too much, I always have a ride home.”
Then the centaur says, “And if I overindulge, he can keep an eye out for the cops!”
The Cyclops says “A bottle of your best, Barkeep! But nothing for my friend here; he’s mean when he drinks.”
The Centaur sidles up to a hot babe at the bar and whispers “I’m so horny not even the crack of dawn is safe around me!”
That, or something very similar, was originated by comedy duo Wayne and Shuster, back in (I think) the 1960s.
A guy walks into a bar. “Bartender, I’ll have a martinus, please.”
“Don’t you mean a martini?”
“No. If I wanted a double, I’d ask for one.”
Shouldn’t the line be “No, those make me see double”? 
No, that was the way the line was delivered by Wayne and Shuster. I don’t know if it is correct Latin, but it sure got a lot of laughs on TV.
Of course, things get muddled in Dorothy Parker’s famous observation:
I like a martini,
But two at the most.
Three, and I’m under the table,
Four and I’m under the host.
Unless you were responding to outlierrn, of course. Never mind, I’ll let my post stand anyway. 
I was, but that’s okay. 
The Cyclops and the Centaur are enjoying their drinks when Hippocrates walks in and orders his customary almond daiquiri.
The bartender looks in the cabinet and sees he’s out of almonds, so he decides to sneak in a substitute.
Hippocrates takes a sip. He frowns and asks the bartender “Is this an almond daiquiri?”
The bartender smiles sheepishly and says “No, that’s a hickory daiquiri, Doc.”
You are correct, it should be ‘those make me see double’, which is a joke because, you know, he’s a cyclops. I not saying it’s funny, but it had a better shot if I’d gotten it right.
The Cyclops sidles up to a hot babe at the bar and says “It’s been a long time since I’ve eaten a Greek…”
The Centaur sidles up to another hot babe at the bar and says “Chiron’s the name, Greek’s my game!”
A Centaur and a Cyclops walk into a bar.
The bartender says “Well, this is a surprise!”
The Cyclops says “How so?”
The bartender says “Well, I heard you guys never use the front door when you can get in the back way!”
A Centaur and a Cyclops walk into a bar.
The bartender says “Well, this is a surprise!”
The Cyclops says “How so?”
The bartender says “Well, I’ve always heard you need a crowbar to separate the Centaurs from the Cyclops!”
Bartender says “Our special today is a shot of Canadian rye.” And the Cyclops says “Well, that sounds better than a poke in the eye with a sharp stick!”
A centaur and a cyclops stagger drunkenly into a bar, which is tended by a guy with a big hump on his back.
The bartender says to the Centaur, “You boys look like you’ve had enough.”
The Centaur is taken aback. “Good sir, I’ll have you know my friend and I are completely sober!”
The bartender rolls his eyes and says, “That’s one I never heard before.”
The Cyclops shouts, “Hunchback! Hunchback!”