Apply grease paint when it is cooler out and not very humid. Humidity slows the drying process. While grease paint doesn't fully dry anyway, it will take longer to solidify at all in a more humid environment.
Prop a fan on top of a ladder or a stool so it is at the same height as the fence. Keep the fan several feet from the fence so the force of the air doesn't cause the paint to smear before it dries.
Turn on the fan and keep it directed at the paint for several hours. The fan will help accelerate the drying process. The paint will still be slightly damp, but the added airflow can help prevent dripping and make the paint slightly less tacky when the paint is first applied.
Wipe grease paint off the fence with a rag to dry the fence more thoroughly. You can partially wipe off the substance with a rag, but you must wash the fence and apply a paint-removing solvent for full removal.