I use Triflow and it works wonderful!! It has teflon in it so it's a little different from regular machine oil. Does you spray can have a teeny straw to help you get the oil where you want it? I have the bottle of oil and also use the little straw.
Don't give up on your Kenmore. I had one that was 'frozen' in many places but I just kept adding the oil, wiggling the part (over and over) as much as it would move, and it wasn't too long before it was moving freely!!