I did a google.com search for Neem oil and black spot. I copied this from a website:

Black spot, caused by the fungus Diplocarpon rosae, produces black spots with feathery or fibrous margins on the upper surfaces of leaves and stems. Small black fruiting bodies are often present in spots on the upper sides of leaves. There is no fungal growth on the undersides of leaves.

The fungus requires free water to reproduce and grow, so leaves should not be allowed to remain wet for more than 7 hours. (When hosing off aphids, do it in the morning so leaves have a chance to dry by midday.) Provide good air circulation around bushes. Remove fallen leaves and other infested material and prune out infected stems during the dormant season. Black spot is usually not a problem in most of California. Miniature roses are more susceptible than other types, although a few varieties are reliably resistant to all strains of black spot. If required, fungicides (such as chlorothalonil or triforine) can be applied preventively. A combination of sodium bicarbonate or potassium bicarbonate plus horticultural oil (as discussed above under "Powdery mildew") or neem oil has also been shown to be effective in reducing black spot.