A lot of good tips in this post. I spent 20+ years building new construction golf courses and renovating older courses all over the country. There are a lot of coins and jewelry to be found on golf courses.
Tees are the best for coins on older courses, when you pull a tee out of your pocket a few coins might spill out and not all all get picked up, I have found quite a few dimes on tee tops. I rebuilt tees on one course that was built in 1910 where I had to strip the grass and topsoil off the top and surrounds and raise the tee 2 feet, then spread the topsoil back over the top. After stripping 6" off and pushing it into a pile nearby I would check the tee and also the pile of strippings. There were still coins in the tee after I removed 6", 100 years of thatch and topsoil accumulation. I did that with 27 tee boxes on that course and found a lot of silver coins and old golf shoe spikes. If it's an older course that has been renovated they would have salvaged any topsoil and placed it back on the renovated area. All is not lost after a renovation.
I went through the same process with greens also, strip, reshape, and replace topsoil. A few coins around the greens but more left hand rings, most golfers pull the glove off their left hand while walking up to the green from where they park the cart, or while walking out of a bunker on the low side (called a walkout and there is a low area at the bunker designed for that) after a sand shot.
Cart path areas near the tees and greens, old outhouse locations, and if there was an old hand water pump over a well are also good spots. On many old courses there was the original snack bar/halfway house that was eventually replaced with a newer one. If nobody knows where that was, take an educated guess.
Permission is best gotten from the superintendent, it's his course, the guys in the pro shop would never allow someone to dig holes on his course. The super may also point you toward piles of topsoil that have been salvaged from little projects around the course. There may be piles at his shop or hidden locations in the woods. Tell him you will fill your holes and they will look as good as when the cups are changed on his greens, he will appreciate that.
I thought I had golf courses all to myself,I guess not. I don't mind sharing a few tips now that I am older and realize I will never get to all the golf couses myself, so go get it guys.
One last thing, if you hear someone holler FORE!!, duck and cover. Good luck.