Li Jian's The Water Dragon seems to match.
Long ago, in a remote village in China, there lived a kind and generous little boy. He spent his days in the forest, collecting wood to trade for food. One day, the boy made a wondrous discovery: a magic stone that caused his money jar and rice crocks to overflow, both of which he shared with the poor villagers.But strange things began to happen. It no longer rained. The crops died. The rivers dried up. A terrible drought had struck and would not release its grip. The brave young boy, full of dreams of a white, water-spewing Dragon, took his magic stone on a journey—and discovered how to save his village.
Found by searching for
children's book "swallows the stone" dragon, which led to this review, which mentions swallowing the stone.
The story of the Water Dragon begins with a young boy, named Ah Bao, who finds a mysterious red stone. He discovers the stone is magical and uses it to help his neighbors in his small village. But no rain falls in the village, everything is slowly drying up, and the red stone’s magic cannot help. Urged by a dream, Ah Bao sets out on a journey to find the water dragon. He makes friends along the way who warn him of a terrible greedy red monster. Ah Bao eventually encounters the monster, who tries to take the red stone. In desperation, Ah Bao swallows the stone and jumps into sea. There he turns into the water dragon, and is able to save his village.