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I've gone to the fishing store( as in hooks) bought lead sinkers. Drilled holes about a 1/32" larger then the sinkers. Put the sinkers in the holes and then swaged them in with a punch.

Another option is to go get a small piece of slate and silcone/ expoxy stick the drift wood to that.

 

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You could also try attaching a piece of plexy glass (acrylic) to the bottom of your wood and put sand on top of the plex glass.
Make sure to use galvanized steel screw so it won't rust.

I would not use a galvanized screw, galvy is just a zinc coating. Infact I would not use any kind of metal screw.