In this we see all the components of a sincere smile (Duchenne Smile) - yet a suppressed one. It strikes many body language novices ironic that a person's teeth need not be exposed in order for a smile to be sincere - although they certainly can be and very often are (When the teeth are visible during a Duchenne Smile - what are the other specific requirements?).
Note the upward vectoring of her cheek muscles - causing the evanescent, concave-up furrow in the lower eyelids. Sister Corita Kent's eyelids are also partially closed - this is profoundly important and missed by most novices (don't look for crows feet - for these are too variable, not very dynamic and your brain is finely-tuned to recognize very subtle changes in another person's eyes). Additionally Sister Corita's forehead is relaxed - without any dynamic furrows (Don't make the mistake of confusing wrinkling of the forehead skin for the deeper muscular contraction).
When the requirements of a true joy-happiness smile are present - the teeth need not necessarily be exposed. Yet her suppressed mouth component in this smile is very sincere. Another obvious sign when scrutinized in this still image (and yet very commonly missed in the dynamics of real-time human interaction) - is the partial covering of her mouth/touching of her lips. If color were present in this photo, we would almost certainly see a nun blushing - and there are clues for this physiology here despite an old black-and-white, low-resolution photo (What is the relationship between blushing and smiling?).
Summary: This image of Sister Corita Kent is highly significant for someone with a high sincerity quotient. She almost certainly was blushing and embarrassed for another person in this moment (Why another person and not herself in this instant?). Her smile is sincere yet suppressed and it is not a requirement that teeth be exposed for a smile to be sincere.
See also:
Nonverbal Communication Analysis No. 3019: Bill Cosby, Rape Allegations, AP Interview - Body Language Tells
Nonverbal Communication Analysis No. 2321: Cardinal Timothy Dolan on "Face the Nation" Problems in Catholic Church & Electing a New Pope Clergy are Not Exempt from Body Language Tells ...
Nonverbal Communication Analysis No. 1559: Timothy Geithner on Face the Nation
Nonverbal Communication Analysis No. 1870: Predicting Boxing Match Based on Body Language Confidence Levels at Weigh-In
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