What is the subjective wellbeing instrument that is used by Science of Happiness for check-ins?
The background of the measure can be found here.
The article implies that it is an ad-hoc measure of emotions created for this study:

Every week, we checked in with our students to see how they were feeling. We showed them a sequence of six cartoon faces created by Pixar artist Matt Jones to convey fear, enthusiasm, anger, affection, sadness, and amusement (below). Under each, we asked them to rate, on a scale of 1 to 10, how much each face matched how they’d been feeling lately.  Then we transformed their collective weekly ratings into a single score.



The result? For students who responded at least 8 out of 10 times—suggesting that they were fully participating in the course—positive feelings went up, and up, and up. They felt progressively less sadness, anger, and fear, while at the same time experiencing more and more amusement, enthusiasm, and affection.
We also invited students to fill out a brief battery of research-validated questionnaires that are regularly used to assess feelings like happiness, stress, flourishing, or satisfaction with life.

The last sentence suggests the ad-hoc nature of the measure (as compared to validated scales). Also, I couldn't track down any published research with this measure. The icons themselves stem from a collaboration of Dacher Keltner with Facebook, as described here, for example.