Jibo Kannon near Fushimi Inari

After a few hours of detective work, I am ready to guess that this is a statue of "Jibo Kannon", with a big hand to chuleta for figuring out that it's a version of who the Chinese call Kwan Yin or Guan Yin (Kannon in Japanese). Yay!

Some (too much?) interesting info:

Jibo Kannon | 慈母観音
Jibo literally means "Loving Mother." Kannon is the Buddhist Goddess of Mercy, one of Asia's most revered deities, and one who appears in numerous manifestations (both male and female). [...] Many have also noted striking similarities between these manifestations of Kannon and the Virgin Mary of Christian tradition. Indeed, Japanese images of the Kannon that show her nursing a baby are not generally considered of Buddhist origin. Instead, such images apparently emerged during the Edo Era, when Japanese converts to Christianity were persecuted and Christianity itself banned.
www.onmarkproductions.com/html/suijin.html#jibo

Jibo Kannon radiates with love and sympathy toward all children and child-rearing mothers. [...] The tenderness of this Buddha is known to nurse healthy children, and also to soothe the devastating feelings of mothers who have lost their loved ones. In Japan, there are many sites with statues of Jibo Kannon, especially sites that celebrate newborn babies and motherhood.
www.onmarkproductions.com/html/child-protectors.html

Statues of Kannon [...] often include a tiny image (Jp. = Kebutsu 化仏) of Amida in the headdress. Curiously, [...] Kannon underwent a change in identity after arriving in Japan. Kannon is male in the Buddhist traditions of India, Tibet, and Southeast Asia. But in China (less so in Japan), the Kannon is typically portrayed as a female divinity. In Japan, the male form was adopted, and it remains the predominant form in Japanese sculpture and art. But female manifestations of Kannon are nonetheless plentiful in Japan. Indeed, a persistent femininity clings to Kannon imagery in both pre-modern and modern Japan. This holds true in Western nations as well, where Kannon is most commonly known as the "Goddess of Mercy."
www.onmarkproductions.com/html/jizo1.shtml

The mudra, or hand position, is the Reasoning Mudra (Jp. = raigo-in 来御印)