You can get metal brackets that slide up under one of the siding panels. The bracket has a hook on it to hang things. I used these at my house and they work wonderfully. I believe I got 4 of the for about $20 online. Expensive for 4 pieces of metal, but they worked well. They were about 1-1.5 inches wide, about 4 inches long. If you search the web for hanging things on vinyl siding, you should come up with something. Something called "the no-hole hook" is similar to what I used. Good luck!

There's a clip specific to vinyl siding the merely slides in between the panels without holes. They only cost a few dollars on amazon. Search "vinyl siding hooks".

Thank you both! I had never heard of those.