This will probably be tricky. Is there no chance you could get a filter for the tank?
I had to keep 5 amano shrimp in a small tank without filtration for a month or so once. I'd buy some
mossballs (they cost maybe £2 each for small ones), and make sure the tank gets plenty of light. Mossballs provide a good staple diet for any kind of dwarf shrimp, provide good aeration for the water (they should pearl with enough light) and help to recycle nitrates and other waste. You'll still need to monitor the water quality carefully (watch out for that ammonia spike!) and make sure you change the water regularly. I'm afraid I don't know how tolerant cherries are to water quality, but this should give them a good chance. Like iSnail says, cherries breed freely, so that could be an issue (though most animals will breed less in poor water conditions).
Also, include a good amount of substrate, ideally a porous gravel. Your tank will cycle itself eventually, and a good substrate will provide good space for the bacteria to grow.
Edit -- actually, I just realised, you could add a little mature filter material to the substrate (provided you have a porous substrate, you could probably just bury it) to speed the process along.
If you can get hold of some, it might also be a good idea to add some catappa (indian almond) leaf to the substrate. Break off a couple of pieces of leaf (they're quite large) rinse and soak so the leaf pieces sink, then just leave them half buried in substrate. These provide further shrimp food and have some antiseptic properties. Oh, one last thing also might be advisable to add a few live daphnia to the tank. Shrimp will sometimes eat them to supplement their diet, but more importantly, they're a good indicator for the water. If the daphnia all start to die, check your water quickly!
This is all from my experience anyway. Hope it's some help.
