Hi Kevin, I'm not related, but since I did look up Eugene Coste's obit for you in the Toronto Star in late 2009, I was interested to read that you are still looking for info and wanted to help you if I could.
Initially, I went on the Toronto Star and Globe and Mail archives hoping to find some mention of Louise Coste's death. I didn't have any luck, unfortunately. However, according to Eugene's Globe obit, she predeceased him (so her death was pre-1940). In the social pages on July 4, 1938, Eugene and Louise's daughter Mrs. Georges Savon is spending the summer with Mrs. and Mr. Eugene Coste, her parents. So it would seem from these two items that Louise may have died sometime between July 1938 and Jan 1940, but I'm sorry I couldn't find anything on her death in the paper.
I did find a couple of interesting items, which you might have already found, in the Globe about Eugene's grandson, Robert Coste, who was the son of E. Frank Coste. Robert was in WWII and was classified as missing and later found. Two interesting pieces regarding this can be found in the Globe: October 2, 1939, page 1 "Fear Upper Canada Grad shot down in Heligoland" and then when he is found: Nov. 4, 1939, page 1 and continued to page 2, col 6: "Swam for hours in icy North Sea"
And a couple of other items of interest:
Jan 18, 1940 page 10 (Globe) Mr. and Mrs. Frank Coste to attend the marriage of Miss Barbara Tims to Mr. Charles Denys Howard
10 March 1948 (births page -- sorry forgot to note page #) Toronto Star: To Mr. and Mrs. Robert M. Coste (nee Virginia Alexander) at St. Michael's Hospital Tesday, March 9, 1948, a daughter.
Hope this helps you a little. Good luck in your searches.