"It wasn't like the first time where she wanted to tell me in a special way," Kennedy said. "No, it was, 'Ian, I'm pregnant.'"
The couple's first child, Nora, was born in May 2011, so Kennedy thought Allison was joking with him.
"I was still asleep, so I kind of rolled over and said, 'No way' and rolled back over," Kennedy said. "And she goes, 'No, seriously.' And that's when I instantly sat up in bed."
The first thought that passed through his head was one that any father-to-be can probably relate to.
"I kind of sat there for a while and thought, 'Wow, this is great, we're going to do this again, this is going to be fun,'" Kennedy said. "She loves being a mom, and I love being a dad. We didn't plan on them being this close, but it's good."
What Kennedy thought about next has no doubt not crossed the mind of any other expecting father.
"The second thought that came into my mind is, 'Gibby's going to give me so much grief for this,'" Kennedy said, referring to his manager, Kirk Gibson. "It's just kind of weird that my second thought when I got the news was Gibby. He gave me a lot of flak for the last one."
By flak, Kennedy means good-natured ribbing from Gibson, who had several of his players become fathers during the 2011 season.
With all the in-season births, Gibson told the team that he was going to have a color-coded calendar made up for them with the green months and red months to help them plan better.
"I never gave it to him," Gibson said of the calendar. "I just threatened it. I told them they could figure it out, it's not too hard."
Once the news sunk in, Kennedy then had to plan the best time to let Gibson know. The couple waited a while before telling anyone, and Kennedy finally sprung the news on Gibson in November after a workout at the team's Spring Training complex.
"He gave me a lot of flak for it this time, too," Kennedy said.
Kennedy reminded Gibson that when Nora was born in 2011, he pitched the next day and tossed the first shutout of his career.
"I did make sure I told him that, 'Hey, it seemed to work out OK the last time,'" Kennedy said. "I thought that might have made him feel better about it, but he didn't seem too happy about it."
That may have been the impression Gibson gave him, but in truth, he was happy for Kennedy.
"Ian is a great family man," Gibson said. "I kid about that, but the reality is not everyone is able to conceive on call, so we certainly welcome our players starting families."
Despite the concerns, Allison came through with impeccable timing in giving birth to Renee Elaine Kennedy.
With Kennedy slated to start Tuesday against the Rangers, Allison went into labor two days earlier while the team was playing at home. So Kennedy was able to be with her for the birth and was able to spend Monday's off-day with the family before flying to Dallas for his Tuesday start against the Rangers.
Gibson's timing wasn't always impeccable during his playing days. While three of his four children were born during the offseason, his son Kirk Robert was born on Sept. 26, and Gibson had to rush home from New York, where he barely made it in time for the birth.
Unlike in Gibson's playing days, teams are now able to place a player on the paternity list and add another player to the roster. A player has to miss at least one day but cannot miss more than three.
The D-backs utilized the list when the wives of outfielder Jason Kubel and first baseman Lyle Overbay gave birth. In both instances, Triple-A outfielder A.J. Pollock came up and stayed one day.
"It's been fun," Pollock said. "I'm just glad they have the confidence to bring me up."
"He's great about it," Gibson said of Pollock. "He's been phenomenal. He's got the right attitude to do it."