We recently got our baby swing back from the last person who borrowed it (I think this swing has been used for over 10 babies), and it took Coco very little time to claim it as her new resting spot. I often find her sleeping in the baby swing, rocking gently, which made me realize we've never had a baby and a pet at the same time so this will be new territory for us. I wouldn't put it past Coco to just hop right in the swing with the baby.
Also, Charlie's presence in this picture is no coincidence. This kid likes to spend every waking moment cuddling with Coco (who unfortunately hates to be cuddled by anyone other than Seth who is - ironically - the family member who was the least enthusiastic about getting a cat). She does a fairly good job of tolerating his affection, but he's also got his fair share of scratch and bite marks.