The extended version of the Hi Hi Puffy Ami Yumi theme song is available on Spotify, but then someone by the name of Imageny tried to upload it, but got a copyright claim from Sony Music Entertainment Japan.
[IMAGENY EDITING] I've reuploaded it on Google Drive. Thank me later. https://drive.google.com/file/d/0Bwmh7PeYtLgzUWduYl9sZFZXTWc/view?usp=sharing