Part came out

You can still sail without it, but you risk losing the daggerboard in a capsize.

Is "the piece" made of metal (with a hole at each end)?

Is the daggerboard made of wood or white plastic?

A photograph would be helpful.
 
image.jpg

The dagger board is wood
 
...and pop-rivets would not be advisable...

"Work" those pop-rivets out and replace them with wood- or sheet-metal screws of 1-inch or more.

A bench vise would speed things along in removal.
 
Is it just me or does it look like those rivets were never properly set?@Debbie , how do the holes on the hull look? If it was riveted, then there may not be a wood backing block for screws.
Looking closer, there are fibers on the properly "set" pop-rivets. Since this is a low tension application, the piece can be restored using expanding drywall plugs and wood- or sheet-metal screws. (Or drilling through two dabs of THIXO, but drywall plugs are $22 cheaper ;) )
 
What is the number on the upper right on the stern of the boat? You could just use a shock cord which allows adusting the board and it retains the board if you flip.
 
What is the number on the upper right on the stern of the boat? You could just use a shock cord which allows adusting the board and it retains the board if you flip.
I probably couldn’t put a shock cord in. I’m not very handy. Unless it’s something super simple that doesn’t need drilling into the boat.
 
Just make a circle out of shock/bungee cord, include the mast & daggerboard.

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I probably couldn’t put a shock cord in. I’m not very handy. Unless it’s something super simple þthat doesn’t need drilling into the boat.
 
Those look like rivets which expand when installed so getting them back in wont work. Is there a block of wood that you can feel with a nail in the holes? If there is a block, I would fill and put in screws. If not you can get new pop rivets, aluminum and if installed correctly will expand and hold the bracket
 
Those rivets are deformed and the deck holes probably expanded a bit when they pulled out, then closed back in, small microfractures around the edge of the hole.

The best approach is too drill out the old rivets and reinstall the eyestrap with new rivets. I imagine some repair needs to be done to the holes also.
 
Those rivets are deformed and the deck holes probably expanded a bit when they pulled out, then closed back in, small microfractures around the edge of the hole.

The best approach is too drill out the old rivets and reinstall the eyestrap with new rivets.
The OP needs something "super simple", which I understood to mean: no drill, no drill bits, no vise, no pliers, no pop-rivet gun, no rivets, no drywall anchors.

Buy 5-feet of stretchy cord ("shock/bungee") cord at a hardware store, tie the ends together, and loop it around the mast and daggerboard. Adjust knot to hold the daggerboard UP.

What year is your Sunfish? I think they started including an eyestrap in front of the daggerboard in the early 1980’s. I have a 1986 and will look to see how it is fastened.
My '79 has the eyestrap.
 
What year is your Sunfish? I think they started including an eyestrap in front of the daggerboard in the early 1980’s. I have a 1986 and will look to see how it is fastened.
My '77 has that eystrap. Not sure if the previous owner added it aftermarket or if it came with it.
 
My '77 has that eyestrap. Not sure if the previous owner added it aftermarket or if it came with it.
My '77 here in NH also has that same eyestrap as my '79.

I think my other three Sunfish are also all '77s: but they're in Florida, so it'll be a month before I can check on them.
 
If you can't fix the eyestrap, just run a 1/8th inch diameter line to the mast.
I find that the eyestrap is mounted way too close to the daggerboard to let me use a bungee to apply tension to the daggerboard to keep it from dropping when raised for reaches or running. I run a bungee all the way from the daggerboard past the mast to the handle on the bow.
 

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