Some daylilies that seem to produce prolifs regularly here:
Longfield's Beauty, Best of Friends, Pink Damask, Gunmetal, Lake Norman Spider.
I will check tomorrow to see if there are others.
I cut prolifs as described by most and root them with the base/root bud just touching the water. Very quickly I get roots around 2-3" long and I plant straight into the ground. We don't get many nights more than 4 degrees F below freezing and the prolifs grow rapidly