It's been forever since I've opened up club lol in my town but I'll try to help out anyway. Did you check with Isabelle for the public works projects? If you rejected to get signatures for Dr. Shrunk, it should appear there as an option, but you did get all the signatures... That's odd though, after a few days of getting all the signatures, club lol should've opened in your town by now.
I tried but I hope others will be able to help you out.
According to the Wiki, it can take anywhere from 4-8 days for Club LOL to open after you turn in the signatures. I remember it felt like an eternity for me because I was so anxious to get K.K. Slider to show up on Saturdays. So, I would give it another day or two and it should open.