Hi Stacey! I would suggest outdoor Command clips. They've worked on every surface I've used them on, and are easy to apply. Be sure they are for outdoor use. I use the clear ones.
You can also buy plastic hooks for this project and hang on your gutter rail. Use year after year.
We have a stucco home and use the gutters and roof line with clips to attach the lights. It has worked wonderfully every year! As far as directly to the stucco wall, that's a tough one. The command hooks typically don't work for me with staying secure.
@Elizabeth Rishel-totally agree! Command hooks may work on smooth stucco, but sure hasn't worked on my house's textured stucco.
I saw a man take a 1/2" pvc pipe and attach the lights to it. Then he just duck taped the "light rods" at each end to secure them to the house.. His home was white so that pvc pipe blended in but you can spray paint it any color you want and duck tape is available in many colors and patterns. I just had an idea.... take red duck tape and spiral it around the pvc for a candy cane effect??They looked so professional and straight! You only have to do it once and then you are set year after year with lights that never tangle and go up 123 easy 😊