Cinesias is the husband of Myrrhine, one of the women taking part in Lysistrata's sex-strike. And he is suffering in a big way because of the strike. It's really hard for him to handle. He's rigid with indignation. He's upset to the bone.
Hey, if Aristophanes gets to make penis jokes, we do too. Fair's fair.
We first see Cinesias when he comes to the Acropolis, where the women are holed up. He is carrying his and Myrrhine's baby in his arms. He also visibly aroused. This (super-awkward) combination is due to the fact that Myrrhine has left the household, leaving Cinesias in the lurch.
Not only does Cinesias have no clue how to take care of the house and the baby, he is also desperate for sex. It quickly becomes clear which of these problems is most important in his mind, when he sends the baby home with a household slave, so that he and Myrrhine can get busy.
In Cinesias's interactions with Myrrhine during this scene, we get a picture of a generally good-natured, not especially enlightened man, who just wants things to go back to the way they were before.
Even though his frustration keeps increasing, it's clear that Cinesias truly loves his wife, and simply wants her to love him back. And of course Myrrhine makes it clear that she does love him; she simply doesn't want to have sex with him until he's signed a peace treaty.
When Myrrhine finally runs away, Cinesias is left totally befuddled. At this point, he does consider going to a prostitute to relieve his cravings, but it isn't clear how serious he is:
Ah, what shall I do? Whom shall I screw,
cheated of the loveliest of them all!
How will I raise and rear this orphaned cock?
Is Fox Dog out there anywhere?
Lease me a nursemaid!
Ah Zeus! The cramps attack anew! (954-967)
He may be begging for a "nursemaid" to come ease his "cramps," but that's the plea of a desperate man. What he really wants is to be with his wife, the "loveliest of them all." Aww.
We see Cinesias's generally down-to-earth nature again after the Herald shows up from Sparta. As soon as Cinesias realizes that the women's sex-strike is international, he doesn't bother fighting against it. Instead, he runs off to tell the officials of Athens, so they can get the city ready to make peace… and make sweet, sweet love.