It is an uphill battle trying to convince the world that the coup benefited Thailand. Sending officials on a world tour to rationalise the toppling of an elected government hasn't worked (except maybe in North Korea, China, Cuba and the like).
General Prayuth should seek support from expats here and use them as spokespeople. How? Bring them happiness. For starters, give them permanent visas, allow them to own real estate, stop overcharging them at entertainment places and allow them to buy booze 24 hours a day, seven days a week.
As a result I’m sure these happy expats would be thrilled to explain (perhaps I exaggerate) to their folks back home why Thailand is in such dire straits. Their explanations should weigh more than those coming from mouths of Thai officials, whose English communication skills tend to be less than adequate.