Hello dontrom,
One thing I can confirm is that the movie you are referring to is definitely not 'The Portrait Of Dorian Grey'. This is a film from the book of the same title by Oscar Wilde and is about a young man who has his portrait painted and the portrait ages, not the young man.
I believe the film you are looking for may be 'Picture Mommy Dead'. This film was made in 1966 and starred Martha Hyer, Don Ameche and Zsa Zsa Gabor.
You can find information about this at:
Picture Mommy Dead (1966)
I believe there is a video available for this film but I can't find much info on the availability of a DVD.
The song I believe is called 'The Hearse Song' and you can find more information on this at:
Mama Lisa's World Blog
I hope I am right. Could you please let me know?
Thanks
Cy