The ornamental design for a part of a cleaner for dairy equipment, as shown and described.
1. Part of cleaner for dairy equipment Design: automatic cleaning device for dairy equipment, in particular for milking devices and teat rubbers; 1.1 shows a perspective view, 1.2 shows a view of the front side, 1.3 shows a view of the rear side, 1.4 shows a view of the left side, 1.5 shows a view of the right side, 1.6 shows a view of the top side, and 1.7 shows a view of the bottom side; elements drawn in dashed lines are only for the purpose of a better illustration and are not part of the claimed design.