Soak tamarind in 1 cup of water for 20-30 minutes. You can speed up the process by using hot water for soaking or by letting it cook in microwave for a minute or two.
Wash Cherries. Remove the Cherry stem.Using a pairing knife make a cut in the center around the seed. Gently twist the cherries by holding it in two hands to separate the two halves. Now you will have the seed sticking to one half. Remove it gently using a knife or your hand. You can avoid all these hassle if you own a cherry pitter.
In a blender/mixie add these cleaned cherries and roughly chopped tomatoes. Grind it to smooth paste. Ensure that no pulp remains. You might want to grind it for a minute or two.
Grind pepper and cumin seeds to a fine powder in a pestle n mortar or a spice grinder. I have used pestle n mortar. I feel it gives a better flavor.
Now extract the tamrind pulp by squishing and squeezing. Discard the tamarind flesh.
In a sauce pan, add oil. When it is hot add mustard seeds and let it splutter. Then add cumin seeds, asafoetida, crushed/minced garlic and curry leaves.
Immediately add tamarind water. You might want to use a strainer to remove any flesh or impurities.
When it slightly starts boiling, add the cherry tomato paste.
Then add pepper cumin powder, salt and red chili powder.
When it is about to reach the boiling temperature add coarsely chopped coriander leaves and remove it from the stove. The trick of making good rasam is not over boiling it.