As you say, "coming from" does not sound natural in this context. That's probably because, although it describes a present state, it does so by referring to something that happened in the past - Tom was born in New York, or Tom travelled from New York.
Tom is a boy coming from New York
Using the present participle like this is makes it sound like Tom is currently travelling from New York. What we actually want to indicate is that Tom was born in New York and at some point in the past he travelled from there. To do this we use the present simple form of the phrasal verb "come from".
Tom is a boy who comes from New York
Present simple is the right tense to use because it defines a permanent characteristic of Tom- it's effectively a stative verb.
Live is also a stative verb, so we can say
Tom is a boy who lives in New York.
In addition, Tom is currently living in New York so we can also use the present participle
Tom is a boy living in New York.
To sum up, the difference is that "come from" relates to a state resulting from something that happened in the past, whereas "live" relates to a current state. Because the latter is a current state, it's OK to use the present participle.