When I was a kid my grandfather, his brother and I dug out the old cistern that was under the back porch of his house. What we did was pump out all the water with a sump pump and then put a ladder into the hole and use 5 gallon buckets and a rope to pull out all the silt. My job was to take the buckets to the garden and dump them. Right away we found bottles, lead soldiers, and old clay marbles(at least 50 of them) so my grandfather decided to dump the buckets though some screen and wash it through with the hose, and that's when we found the coins. I can't remember what all we found as far as coins (this was 30 years ago) but since then I've gone to the garden site with my md and found a few that we missed including some silver. I've only dug out one other cistern since then with similar results and if I got the chance I'd do it again any time. That cistern I think, is what got me started on treasure hunting.
I have to say though these things can dangerous, they were usually not built with the highest quality brick and most will have deteriorated over the years. I have a buddy who got a nasty gash on his head and a concussion from a dislodged brick, so I'd have a hardhat on inside. Also tie a rope to yourself so the guy up top can pull you out if it does collapse on you. Another thing to keep in mind is that there's no telling how deep the silt is so probe with something to find the hard bottom before you climb in.