Dulcimer2, I used to sing many songs to my mom. The two that jump into my mind are "Mammie" and "Danny Boy." I used to get down on my knees and take her hand and sing as warmly as I could. I started singing those at an early age so it was something she was used to as I would try to cheer her up as well as a special "I love you" to her.
I would have to say that you and your sister must think about this together. Think about what your mom loves, what memories you all share. Sometimes, a song can be a "mom" song without it being one that another person outside of your family would think of. What's important is the thought and emotion behind it. For example, "The Coat of Many Colors" was a song that held great signficance to my grandmother and my mom used to sing it to her.
After my mom's death, my stepdad and I found another "mom" song- "I'll Be Seeing You."
Congratulations to your mom- you're very lucky and from what you've written, she's lucky to have had such great children! :)