"Please sit down there."
I think で works fine here.
The only difference the two particles being one of intention, as in そこで座る would imply active action or intentionally acting in order to sit down, while そこに座る would better describe the state that someone is in. (で tends to be used with more active verbs)
So example, if someone is already sitting somewhere you could tell them はい、そこに座ってください as confirmation, "yes, please sit there." Or you could have a situation where you're instructing a person to move to another table and then you tell them はい、そこで座ってください to them "(now after the preparation for this) yes, please sit there"
そこで doesn't work here because the sentence is sit down there, that is a direction where to. ("To there", if we ignore English grammar.) That's why we use そこに.
With そこで this sentence would be "Please sit there", which only shows the place and not direction, which is implied in the English sentence by using "sit down".
I feel like it should only be "please sit there." To avoid confusion because you don't say "down there" in Japanese even though it can mean approximately the same thing in English to say "down there" unless I'm wrong but they definately don't say "sit down there" in this sentence; it's just "sit there". Like it should accept "down there" but the English sentence should be shown as "please sit there" because that's a better translation