Charismatic Conquerer triggers, causing you and an opponent to copy it.
Resolve the opponent's copy of Charismatic Conquerer, and then resolve your copy of Charismatic Conquerer.
When your Charismatic Conquerer token enters the battlefield, the opponent's Charismatic Conquerer triggers, causing you to tap your Charismatic Conquerer token.
Resolve the original Charismatic Conquerer spell.
When the nontoken Charismatic Conquerer enters the battlefield, the opponent's Charismatic Conquerer triggers, causing you to not tap the nontoken Charismatic Conquerer, and causing the opponent to create a 1/1 Vampire creature token.
When the opponent's Vampire token enters the battlefield, both Charismatic Conquerers you control trigger, causing you to create at least one 1/1 Vampire creature token.
When your Vampire token enters the battlefield, the opponent's Charismatic Conquerer triggers, causing you to not tap the Vampire token, and causing the opponent to create a 1/1 Vampire creature token.