get_pref_center.py

import json

latitude = 0
longitude = 0
pref_name = "福島県"

with open('prefectures.geojson') as f:
    j = json.load(f)

for feature in j["features"]:
    if feature["properties"]["name"] == pref_name:
        coordinates = feature["geometry"]["coordinates"]
        points = [p for i in coordinates for j in i for p in j]
        break

for p in points:
    latitude = latitude + p[1]
    longitude = longitude + p[0]

print("{}, {}".format(latitude/len(points), longitude/len(points)))