The safest strategy, both from an engineering and environmental viewpoint, is not to fill a sinkhole. If the sinkhole is a hazard to livestock, put a fence around it. If filling the sinkhole is essential to your project or the sinkhole is a danger to people, there is a right way to do it. The sinkhole can be filled using a graded-filter technique (Reitz and Eskridge, 1977; Sowers, 1996). The purpose of the graded filter is to allow water to seep into the ground while the soil is held back.
Always consult a professional geologist who is experienced in identifying karst subsidence and an engineer experienced in sinkhole remediation when dealing with any structure threatened by a cover-collapse sinkhole.