The past tense of administer the coup de grâce is administered the coup de grâce.
The third-person singular simple present indicative form of administer the coup de grâce is administers the coup de grâce.
The present participle of administer the coup de grâce is administering the coup de grâce.
The past participle of administer the coup de grâce is administered the coup de grâce.