The ringtone could be the sound of a magic key. In the bedtime story, a child finds this key which has a 'ring ring' sound. Every time the key rings, a door to a different story world opens. This way, the ringtone is not just a sound but a crucial part of the adventure in the bedtime story, making it more interesting for the kids.
One way is to have a character in the story, like a friendly alien, whose spaceship has a unique ringtone. When the kids in the story are ready for bed, the alien's ringtone plays and he starts to share his intergalactic bedtime tales. The ringtone can add an element of mystery and excitement to the story. Another way is to have a magical ring that when it rings (makes the ringtone sound), it transports the characters to a world of dreams and stories. This can make the bedtime story more engaging for kids as they love the idea of magic and adventure.
You can make the ringtone be a signal for a special event in the story. For example, in a story about a group of animal friends, the ringtone could be the call from the wise owl who gathers them every night to tell a story.