Fortunately, Positive Psychology does not promote the elimination of negative thought or critical thinking. These are important for us to keep safe and protected in environments that can be unpredictable. What is does do, however, is provide a framework to put these negative/protective thoughts into proper perspective. One of the main tenants of positive psychology is that while negative emotions are felt more strongly than positive emotions, most people experience much more positive events in their lives than negative ones and if a person is aware of the these positive events, the increased number of them 'off-sets' the high emotional charge of negative events leading to a balanced emotional state. This can be difficult for those who think in extremes or have trouble picking up on subtleties, but I believe that an acceptance of positive thought can be developed in the same graduated experiential way that many other adaptive, communication, and social skills are increased.
In the beginning, let's start small. Have the person with ASD think of one positive experience each day and communicate it in the best way that they are able (speaking, writing, pictures, etc.). The person may need some suggestions of positive events to get started or they can use their personal interest, although it would be helpful for the person to identify positive events outside of personal interests as well. Once the positive event is identified, have the person relate how it made them feel. Even if the response is just "good" that's an important place to start. Over time the number of daily positive events can be slowly expanded. Ideally, you'd like a ratio of at least 3 positive events/thoughts to 1 negative event/thought. Highly optimistic people have a ratio of about 5:1. Once the person begins to think more positively, then the opportunity for greater perspective regarding the negative emotions can be achieved.
Steven C. Altabet, Ph.D