(Thanks for including the card text! Helps a ton!)
Note that if it were not for the "if able" text, you would have to choose a character that was able to be declared as a defender (i.e., standing and has the right icon) because normally, you cannot trigger an ability that has no ability to change the game state.
As worded, though, Dornish Paramour allows you to choose characters that are not eligible defenders at the time she is declared as an attacker, but could possibly become eligible (for example, gains an icon or is the target of a standing effect) before defenders would be declared. That "if able" greatly changes the character and usefulness of the card!
Ok, that clears up a question I went here to ask actually. It seems that people are declaring the chosen character as a defender right away when it gets targeted by the Paramour rather than waiting for the declade defenders framework action window to declade defenders. So in practice if the Paramour chooses for example Margaery Tyrell (Challenges action: Kneel Margaery Tyrell to choose a character. Until the end of the phase that character gets +3 STR) as the target, you could use Margaerys ability to boost another character in the action window before defenders are declared and thus make her unable to be declared as a defender, is that correct?
Also what caused the question was also how the Paramour interact with an effect like Highgarden. From what I remember when I last played there was a rule that whenever there were no longer any participating characters in a challange the challenge ended then and there before defenders could even be declared which meant you couldn't declade defender and win on defence if there were no longer any attackers unless you waited until after defenders were declared to remove the attacker. Am I remembering that correctly? At any rate that seems to no longer be the case? Since the RRG states that a challenge is considered resolving until step 4.2.6 and it doesn't mention any exceptions to that rule as far as I have found. So that mean you can now remove or kill all attackers and then still be able to declare defenders and win on defence?
Also what happens with the lasting effect of the Paramour of she is removed from the challenge before defenders are declared? If the challenge still resolves which it seems it still does then the chosen character will still have to be declared, if able, I'm guessing?