When I put Amy to bed for her afternoon nap, it usually goes something like this. The curtains in her room are closed and a path is cleared on the floor (if necessary) from the door to the window on the other side of the room.
I take Amy into my arms so that she lies on my right arm with her head cradled in my elbow and her feet hanging down, with my left arm between them and holding on to my right to help support her weight. Then I hum sungs while carrying her through the room: back and forth and back and forth and….
She's usually quiet as soon as I pick her up. After three to five minutes, her eyes are usually closed; after three to five minutes more (to give her time to fall asleep properly), I put her in her bed. She'll often roll over or open her eyes briefly but will resume sleeping almost immediately, and will wake up again after about two hours.
On the other hand, when Stella puts her to bed for her afternoon nap, it usually involves at least half an hour and lots of screaming, so I'm told. (This usually only happens when I'm away; if I'm there, I'll usually be the one to put her to bed.)
What also sometimes happens is that one of us will put her straight to bed, and she'll be quiet… then later get up out of bed and play in her room rather than going to sleep by herself. (This sometimes happens at night as well, where she'll sometimes get up again and play by herself before going to bed when she's tired enough—or falling asleep on the floor, as has happened occasionally. But she usually stays in bed in the evening, while if I don't sing her to sleep, she'll get up more often than not if put to bed at noon.)
Singing or humming also tends to calm her down in other situations, too.
I'm not sure why she'll let me carry her around humming to her in order to fall asleep but won't let Stella do so: apparently, whenever Stella has tried this, Amy will twist around and try to escape, or try to get under Stella's pullover to have a drink, or otherwise vehemently display a complete lack of interest in falling sleep.