There's a guaranteed way to recruit any prisoner, but there's no set time limit: keep your Wardens' moods consistently at "Content" or "Happy" for an extended period of time. Sooner or later, they'll get the "Inspired Recruitment" event...which guarantees a 100% chance of recruiting on their next attempt.

Since there's no set time as to when this will happen, put the prisoner into a Cryptosleep casket, where nothing stupid will happen to them (like getting shot to death during a jailbreak). Give your Wardens plenty of joy activity, lavish meals, and get their moods way up. When you get the "Inspired Recruitment" event for one of your Wardens, get the prisoner out of Cryptosleep, make sure none of your other prisoners are eligible for recruitment, and take all other potential Wardens temporarily off Wardening...your Inspired Warden will then recruit your prisoner with 100% success.

You have to be patient, but this is a LOT faster than trying to recruit a prisoner who's at 99% difficulty, in my experience...even if the prisoner is happy.