Let's assume a very small moon of Earth in circular orbit with a radius of 10,000 kilometers = altitude about 4000 kilometers, speed about 7 kilometers per second. C = 6.38 times 10000 = 62,800 kilometers.
A tether about 4000 kilometers long, spins about the tiny moon at 25,000 kilometers per hour, at the tip. Divide by 3600 = 7 kilometers per second = same as the orbital speed of the tiny moon. That means the tip is approximately stationary just above Earth's surface at about 110  minute intervals. It would touch the surface except the tether is not exactly straight, for a variety of reasons. We reel in a bit of the tether at the tiny moon, if it is predicted to touch Earth's surface. At each close approach we can attach a small payload, giving it an upward push, if the stretching of the tether (due to the extra weight) is likely to cause it to drag on the ground or dangerously stress the tether. A computer can make these predictions with the help of sensors on the tether which keep track of transients traveling on the tether. About 55 minutes after attaching the pay load, it is at the top of the arc at an altitude of about 8000 kilometers; this time the speeds add instead of subtract = 14 kilometer per second = fast enough to fling the pay load to anywhere in the solar system plus or minus a few degrees of the plane of the tips orbit at release. This will be difficult to predict precisely as there are transcients traveling on the tether.
The main problem is the payload will be subject to perhaps 10 g for about a second, shortly after attatchment, and to several g throughout the 55 minutes. Also important, the tether may fail during the the peak acceleration, unless the portion of the tether near the tip is very strong.
The energy is not for free, so the tiny moon must have lots of solar panels and/or a nuclear reactor, so the tether can be boosted electro-dynamically. The tether travels at supersonic speed in the upper atmosphere, so there are sizable friction losses heating both the payload and the tether. Cooling the payload to -39 degrees f = -39 degrees c may be sufficient to avoid over heat problems. A longer tether to a tiny moon at higher altitude reduces both the g loading and the heating. Apparently the upper limit is about 17000 kilometers as this would barely clear the GEO synchronous orbits. The longer the tether, the stronger the tether material needs to be, but the strength requirement does not increase rapidly and is less than required for the space elevator. Please comment, refute, and/or embellish.   Neil

Healthy people can survive 10g for a second, fighter pilots are tested for this.

The speed in the atmosphere will have to be examined to avoid major problems with air resistance.  I suspect that the touch down point may move around so the cargo may have to be launched from an aircraft.