This is the basis of the problem of foot roll in building bipedal rigs. There are two approaches commonly used. I'll describe a stripped down version of the simpler of the two.
The above three bone rig is called the rocking rig. The head and tail of the rock
bone are the two pivot points. The parent
bone serves to avoid the problem of parenting. The control
bone is the rocking bone.
This rig works by rotating the control
bone on its local Z axis, currently oriented along the world Y axis. It is usual to lock the rotation of this bone. As the bone rotates counterclockwise from its center position, the rock
bone will rotate counterclockwise on its head. As the control
bone rotates clockwise from its center position, the rock
bone will rotate clockwise on its tail, as a result of being parented to the parent
bone.
The positioning of the bones is critical. They must lie in a line on the same axis, in this case the X axis. The head of the parent
bone must lie in the same position of tail of the rock
bone. This is one of the two pivot points. The other pivot point lies at the head of the rock
bone.
It is convenient for the control
bone to be parallel to the parent
bone and for your purpose for the parent
bone to be perpendicular to the rock
bone.
None of the bones are connected to the others.
The orientation of the axis of the bones matters. They should all have their Z axis parallel to the world Y axis and pointing in the negative direction.
The parent
bone is the parent of the rock
bone. This is so that rocking the rock
bone on its tail will work. The parent
and control
bones are unparented, although in a rig they would normally both be parented to a root bone.
Each of the rock
and parent
bones have a copy rotation constraint to copy rotation from the control
bone. Each also has a limit rotation constraint. The limit rotation constraints are what divide the rotating between the two pivot points. The constraints all operate in local space.
Here are the constraints
For the rock
bone:
For the parent
bone: