Cardboard might be a bit extreme, even for daffodils. A few layers of newspaper would seem more reasonable.

George

Mulch! This is what mulch is for. Smother the area in a couple of inches of mulch. As George says, lay down a few layers of newspaper. Wet it so it stays down flat. Then put bark mulch on top of that. Since the weed seeds are already sprouted, some may push their way through. Pull those that do. By spring the newspaper will have rotted. The daffodils will push easily through the mulch.

Be careful with the newspaper. I tried newspaper under mulch in a bed of shrubs leading up to my front door in Florida and it ended up either attracting fire ants. In South Carolina, I was given some Crinum bulbs. The donor dug them up with a shovel and the rootballs had lots of soil still attached. For transport, I brought along some cardboard boxes. I wasn't sure where I wanted to plant them and thought I would dig a trench in my garden, place the boxes in the trench and back fill around them with soil. Then, when I decided where to put them, they wouldn't have put down roots so to speak and would be easier to lift and move. One word. TERMITES. They loved the rotting cardboard. Thankfully, it was a good distance from the house.

It probably depends on where you live. No fire ants in the midwest (thank heaven). And if termites were around, I'm sure they would love my mulch too. But everyone around here seems to use bark mulch, and I've never heard any alarms about termites. I've been more concerned about it attacting slugs. Your experience might be unusual (I sincerely hope so...)

I agree, newspaper and mulch...the amount of paper and mulch would depend on the size of the weeds. If they are really small a shallow layer should do it.

Preen is my friend to keep weed seeds from germinating in beds. I use it both under and over the mulch, and things will stay pretty weed free for the season.

I don't have anything in those beds that I want to reseed itself.

Sue