ericosmith,
One private CG would be The Christian Conference Grounds Campground just south of Grand Haven, MI. 118 sites with 30 or 50 amp electric right on Lake Michigan with a very nice pure golden sand beach. Another could be the small Elks Club (BPOE) CG just north of PJ Hoffmaster State Park between Grand Haven and Muskegon on Lake Harbor Rd. I'm familiar with these 2 private CGs. Another one is down south of St. Joseph called The house of David CG. A few more private CG's on the Lake Michigan lakeshore in the northern half of the Lower Peninsula.
You won't find many private CG's on the West Michigan Shoreline south of about Whitehall, MI because the land is worth/sells for so much money. Usually a min of $6,000/front foot on Lake Michigan if it's perhaps 50' above the lake to even $15,000/front foot if it's pristene beach land. That's just for the bare land large enough to build a home on (100' wide X 250+ deep) as there's min setback requirements from the highwater mark. That's if you can find some bare land privately owned that you'd like to purchase. That's why most CG's right on the the shoreline are State Parks or County Parks etc and have been so for over 50 years plus. Several Michigan State Parks date back to 1921. Grand Haven State Park dates back to the 1920's. Not much of the lakeshore real estate was owned back then and the state has been buying up stretches of lakeshore land ever since and making it into state parks so everyone has access to the beaches.
You can just imagine how much they'd have to charge per night on a site to having to buy the land and build a CG there. In the northern half of the West Michigan shoreline, the land sells for less but is still very expensive.
Just looked up the Grand Haven Christian Conference Grounds and there's now 140 sites in section A,B,and C. Section A (101 campsites) are full hookup $35/day. B & C are electric and water and are $30/day. Yup, it does fill up fast and reservations are free, almost necessary! Must be made a min of 48 prior to date wanted. Handicapped accessible, clean restrooms and individual showers, small restaurant and an ice cream store, has laundry facilities and a beautiful beach.