The coins and rice are offerings for the stone images of Buddha. These stone images are set inside the grounds of Yakumo Shrine. It's been here since 1778, the Anei Era.
Usually the rice is offered first, because rice is the source of life for us. Many people also offer coins, especially the 5yen coin (the one with the hole). The Japanese word for '5yen' is 'Go-yen,' which is similar to the word 'Go-en,' which means 'fate' or 'luck.' So because of this play on words, many people offer a 5yen coin at shrines.