Redesign the container so it has handles, grips, or handholds.
Hold the container close to the body.
Don't carry more than you can handle. To reduce the weight of the load, use a smaller container.
Wear proper size gloves that fit. Gloves with rubber dots on the surface can increase grip stability on slippery surfaces.
Increase the size of the bucket or pail handle with padding or a clamp-on handle.
Get co-worker assistance when necessary. Discuss your plan so you don't have surprise movements.