If you're looking for anime similar to Yasashi-sa no Tamatebako, you might like these titles.
The official music video for Chiisaki Mono-tachi by MAN WITH A MISSION that was featured on NHK's Minna no Uta program.
The official music video for Minarai Chameleon by Dario & Tomoko that was featured on NHK's Minna no Uta program.
The official music video for Daijoubu by BERRY GOODMAN that was featured on NHK's Minna no Uta program.
The official music video for Ohayou Crayon by Hiroko Taniyama that was featured on NHK's Minna no Uta program.
The official music video for Arigatou: Kokoro no Bara by Mike Maki that was featured on NHK's Minna no Uta program.