Not necessarily the nicest thing, but I remember my mom used to offer this as a solution to many of the parenting problems we presented her with-
me - "my brother won't share the legos"
mom- "if you two can't work it out, we'll have to put the legos away. One of you can scrub the toilet, the other can scrub the grout."
me- "i'm bored"
mom- "i'll give you five minutes to find a way to entertain yourself using your books, your crayons, your blocks or your imagination. If you can't come up with a solution, you can peel the zucchini, that will cure your boredom and give you something to do."
Me- "I'm bored."
Mom- "Pleasure to meet you 'bored', my name is Mrs. F. B., how do you do."
me- "no mom, I'm feel bored."
Mom- "glad you are in touch with your feelings. you can't figure out what might be entertaining for you, you can go play outside, or you can sit in your room until you feel otherwise."
Mom was unrelenting. That said, we were enrolled in, and willing participants in a number of activities. Not sure when we found time to be bored. But then again, kids will be kids. Poor Mom was probably exhausted keeping house, playing taxi, and wasn't willing to shoulder this problem too.
Good luck to you and yours,
F. B.