First, the note on semantics/vocabulary:
You DON'T reject a job offer, you decline it. If you don't know the difference,it's your problem.
Second, the tutorial on the reason for cooling periods:
A cooling interval is appropriate if you applied for a position and got rejected for that position - There is no point to being rejected again by the same people for the same reason. However, don't conflate that circumstance with you declining a proposition for an interview.
Third,regarding your specific question:
There is no reason why you shouldn't be able to change your mind about interviewing with a prospective employer within 24 hours of either your circumstances changing or your perception of your circumstances changing. You simply write them,using their contact info, notify them that your circumstances have changed, and ask them to schedule an interview. That's assuming that you declined the original invitation for your interview and that you didn't reject it,of course - Being perceived as rude does not usually open doors for you.