Only poorly thought out ones...
Wilson will not care about the black vote. He was alive during the ending of the US Civil War, and him mother refused to sleep in the Lincoln bedroom at the White House. Also, at this time most African Americans vote Republican. I doubt the money the US could lose was a lot, but it is the principle, I suppose. That last sentence is irony.
What raw resources does Haiti produce? WW1 will increase food demand, but the 1920's glut and the Great Depression will ruin the party. A problem is the US was irrationally worried about German influence at the time. Either the German immigrants have less influence, or the US more. Maybe the ban on foreign ownership can be gotten around by the US floating bonds with fixed dividend, err I mean interest payments? A savvy diplomat/politician could make it work.
My POD's are either: Teddy wins 1912, appoints Taft to run Haiti. He does ok; does not dismantle French education system but sets up vocational schools for the lower classes. Upper class is marginalized (not really necessary, more to diminish German influence). NYC finance breaks into Haiti by rolling over all debt at low rates (German immigrants charged higher rates). That means more current funds for bettering the needs of Haiti. Also to break upper class, poorer (not much) non mulattoes (full blacks? not sure what they are called) are given responsibility (the US declined to let the Haitians run Haiti). Can't think of any other POD's for this option.
2. A Progressive, non-Teddy wins (anti-imperialism, strong Christian needed. WJB?). The Philippines are let go. Haiti is ignored, especially with voodoo practiced. Still has debt, coups, and the Depression to deal with, but at least Haitians get to decide.
3. OTL, but Wilson fears Teddy, and his new Rough Riders. Says something about "blacks helping blacks, with white guidance" (might not be word for word...) so FDR and Teddy, plus the Rough Riders, are sent to Haiti instead of France. This POD might be too late, honestly, but it feels fun.
The Rough Riders are only for defeating the rebels, and do not shoot unarmed people. Black officers help give the US some good PR. Teddy sees this as another Philippines (very bad), but FDR keeps him on a leash. The US political dynamics mean the US is more moderate, and follows more of option 1. And for fun, when Wilson leaves the Republicans behind in 1919 (when he goes to France), they pass a bill that says the US will pull out of Haiti within 18 months, out of spite.