I'm not sure how long it would take for your kids (how old are they?), but I'm pretty sure that once my kids hit elementary age if I told them any mention of boredom would lead to work - and then followed up on that threat when they said they were bored - I wouldn't hear from them again for at least a month. Maybe two.

How old are your kids?

If you spend a couple of hours (cumulative time, not all at once) assigning them various jobs, and then assigning another when that job is done - I don't think you'll have them come back Monday asking for more.

Maybe make a list of chores over the weekend - let them know Sunday night that any mention of boredom Monday will result in them being assigned one or more items on the list.