Contact local businesses, businesses that the charity uses extensively (lawyers or builders, perhaps) and wealthy individuals and ask them to sponsor a tee. For the cost of a simple sign and the time to generate a receipt with the charity's tax ID, you can generate significant funding. Remember to have these placed on the course prior to start of the tournament, but not so early that they get wet with early morning dew as this can ruin the signs.
Food and Drink Sponsors
A golf tournament typically involves libations and some good food. Local businesses, especially sports bars, may be willing to supply food or drink, or to cover the cost of providing these items. This minimizes the cost of the tournament and increases the payment to the charity.
You can generate significant sales from raffling off items that golfers might enjoy. Work the golf club and see if they can get donations of foursomes at other courses. You might also see if the chef at the course will donate a catered dinner. Other items that typically raffle well are tickets to sporting events, which can be donated by the community or the team, and home electronics equipment.
Typically at the end of a tournament, you hold a reception to congratulate winners and socialize. During this time, you can generate more income for your charity by running a silent auction. You might include gift certificates to restaurants, spas or shops as well as items, such as new golf club or bag.
Closest to the Hole
You can also run a contest to see who can putt closest to a designated hole. Have the pro set the hole and the distance from which you putt. Golfers can pay a small fee for two or three tries to putt closest to the hole. You can offer to split the pot with the winner, or simply keep the proceeds for the charity.