"I wouldn't be surprised if that doesn't happen real soon," the actor, 39, told PEOPLE at Thursday's Zodiac premiere in Hollywood. "We're seriously in heaven with the kids."
Ruffalo and Coigney, 34, owner of L.A. boutique Kaviar and Kind, wed in 2000 and are parents to son Keen, 5, and daughter, Bella, 1.
And Ruffalo has his daddy rituals down pat: "I make them French toast a few times a week, which they dig. They'll pitch in on that. Bathing and reading to them at night and singing to them – the little things. I take my son to baseball practice and that kind of stuff."
The best thing about fatherhood? "When they curl up on you, they want to get in your lap or lean up against you. Just playing with them, the day-to-day stuff – when they come in the bed in the morning is really nice. Sometimes it's not so nice because it's really early! It's all the sweet, gentle things that they bring to your life – and their innocence."
Ruffalo struggled for years trying to break into show business, working in L.A. restaurants before winning fans with 2000's You Can Count on Me.
"I'm getting older, so I don't hate myself so much," he told PEOPLE. "The struggle, as difficult as it was when I was younger, I have a lot less angst about that. I can pay the bills. My cars don't get booted and taken away from me periodically anymore. The credit cards work when I try to run them through. I've got two kids and a beautiful woman. I've got a lot of gratitude."
Asked if he and Coigney have time for romance despite busy careers and two young children, he said, "Yeah, we do, we try. Probably once a week, or a few times a month, we try to have date night."
But as Ruffalo told reporters, the Zodiac experience recently got in the way of some romantic time: He freaked out during a trip to the mountains with his wife.
Click play to hear Ruffalo talk about it: