I’m really bad at turning people down. In a role play I’m hosting, someone asked to be a character that’s already taken. How do I nicely let them know the character is taken?
Just say: “Sorry, that character is taken. Here's the ones that are still available.”
Having played various games online or in person this is all that really needs to be said. It's fine and polite and should be non-confrontational. If the person kicks up a huge stink about it, it indicates they'll probably be a bad fit for your environment anyway, and you can disinvite them from the game or otherwise not proceed with them. The player is now informed about their remaining options and can make a new choice.
If there is a public list of available characters, it helps to mark which ones are taken and/or which ones are still available so as to help avoid clashes like this. It's been the norm for my online games to have a document listing the players and the characters they have chosen. The same document provides the remaining available roster.
If you've got a potential enormous world, e.g. you're all playing on a large spaceship but it's the Chief Engineer role that's already taken, it is helpful to give a brief overview of what kinds of roles are available and list which ones are filled/taken.
Understand the transaction here
I gather they know the character is taken.
Regardless... The transaction is "Even though this character may be taken, I would rather play that anyway. Will you be able to effectively DM this game if two of this type of character are in the party?"
So it's not "asking for permission on a matter where you have fiat". It's "asking if your planned adventure will be able to support this and if you will be able (and willing) to facilitate that".
That is more of a self-assessment question, with an answer "yes" or "no".
No different than a private pilot "can we bring my weightlifting set on our trip". The pilot doesn't need to agonize over saying no, merely assess whether it exceeds flight minimums or his personal minimums. So it is for you: either this adventure works that way or it doesn't.
Characters can't be taken...
In most RPGs, there is no rule specifying that two players cannot have similar characters. It is entirely permissible to have multiple players (or even an entire party!) of the same class, race, or race/class combination.
Because those players will give their characters different backstories and personalities, roleplaying them differently, the characters will diverge significantly, despite some similar mechanical elements. Not every dwarven barbarian is the same!
Unless you decide they can
Of course, the exception to any rule is 'if the GM decides otherwise'. If you, for some reason, don't want this to happen, then the correct way to express your preference is as a preference: "Hey, I'm sorry, but I'd prefer if you chose a race/class/race-class combination that was unique—someone is already a _____ and I'd rather not have two.'
If no-two-characters-alike is a rule of your particular RPG, then point them to the rulebook.
Finally, if some feature of your game makes it possible for characters to be 'taken' (e.g. there's a list of pregenerated characters they must choose from) then it should be obvious to them that they may have chosen an unavailable character. Telling them someone already picked that one is unlikely to cause significant surprise (though disappointment is a possibility).