I originally posted this question as a guest and am unable to select an answer, however, thanks to everyone who posted here, I have my answer and I'd like to share a little information with you all on the topic.
World Wide Games of Colchester originally made the game. It was indeed called "Fore Par", and it included wooden pucks with little rubber rings on the outside of them to help them bounce. It was a large, plain wooden board (the exact dimensions of which I am still trying to pin down) with pegs and recessed "holes". At one time, the game sold brand new for $158.50. Here is an archived article from the NY Times that mentions the company and the game and cost, as well as other games made by WWG: http://www.nytimes.com/1989/03/12/nyregion/from-adi-to-skittles-to-yoot-making-fun.html
In some instances, Fore Par was included in a "cabinet" set of games you could purchase from World Wide Games.
World Wide Games was eventually purchased by S&S Worldwide. Sometime later, SSW would build a similar game known as "Bumper Golf". I didn't recognize the game because of the graphics and I thought for sure they weren't the same game (since it didn't use coins), but since I found a picture of the original Fore Par, I've been corrected. In fact, looking closely at both of them side by side, you can see that the layouts are EXACTLY the same, the only difference being the starting point for the 4th hole is shifted slightly to a different position. (See photo).
I wish I knew a little more history about the original Fore Par game, and a history of the company World Wide Games. Seems they cared about making a quality product that was used by many educational institutions (schools, YMCA's, etc). It makes perfect sense that I originally played this game as a child at my elementary school.
At my school, the wooden pieces were long gone, and the board had been played with coins for many years. So long that years of coin-impacts had worn away at the wooden sides and hazards at the best places to bounce the pieces.