There is also a wonderful torch song cover of "Ame nochi Ame nochi Ame" by trans artist Ataru Nakamura, (中村中) I couldn't find that either, but here is the original song itself.
And best of all in a way, there is a cover of こいのうた (koi no uta, "love song") by Mongol 800, which is funny as one of their own famous songs is ちいさなこいのうた (chiisana koi not uta, "small love song")
I encourage you to listen to the very end.