For example, "I can put you down on a weekend tour." As far as i know, when you use the phrase "Put you down" it's more of embarrassing someone or it could also mean that you want to kill that person.
What do you guys think?
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Put down meaning kill is only ever used of an animal. It would not be understood in that sense in referring to a human, and if you found a way to force that meaning it would imply that you were regarding the person as an animal.
However there is another idiomatic meaning which could occur here, meaning "deprecate", or "diminish in status". I don't think anybody would read that meaning into this example though, unless there were some very unusual context.
Merriam-Webster lists eight different definitions for the phrase "put down".
When someone says they'll "put you down for a weekend tour", they mean they'll write your name down in the list of weekend tour bookings. Or maybe instead of writing it, they'll type it, or drag it there. They'll put it there somehow.