not sure of year, prob. 40's - 50's, the subject of the movie is a
little girl who plays piano, who's mother is away, the father hires a
nanny who cares for the little girl, mean while the mother becomes
sick and as she is  on her death makes the decision for the nanny to
fall in love with her husband and daughter to know that her daughter
will have a good mother when she dies. The nanny asks the little girl
after the mother dies, what is the one thing you remember about your
mother and the girl looks up to the nanny as she plays the piano and
says "Her smile".
I was thinking the name of the movie was "Sing me No Sad Song" or Play
me No Sad Song. Not sure who the actors were.

Hi Vienna54,
  
I believe the movie is "No Sad Songs for Me" (1950), starring Margaret
Sullivan, Wendell Corey, and Natalie Wood.
  
"No Sad Songs for Me" (1950)
http://www.imdb.com/title/tt0042790/
  
  
Plot summary:
  
"Mary Scott (Margaret Sullivan) learns she only has ten months to live
before dying of an incurable disease. She manages to keep the news
from her husband, Brad (Wendell Corey) and daughter, Polly (Natalie
Wood.) She tries to make every moment of her life count, but her
effort is weakened by the discovery that Brad is interested in his
assistant, Chris Radner (Viveca Lindfors). But when she learns that
Brad does indeed love her and not Chris, and that Chris is leaving
town, she realizes what she must do to ensure the future happiness of
Brad and Polly. She persuades Chris to stay, makes a genuine friend of
her and watches Polly grow towards Chris."
  
Internet Movie Database: No Sad Songs for Me
http://www.imdb.com/title/tt0042790/plotsummary
  
  
Search strategy:
  
I searched the Internet Movie Database for movies with "sad" in the title.
  
  
I trust this is the right movie.

this is the movie, thank you so very much - My mother and I watched
this together when I was a child.We both have been searching for the
title so that we may buy the movie.