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First of all you would need to know their date of birth and when and where they died. Sometimes people coming to the US changed their names to make them more "Americanized" so that they fit in more easily. For instance, Peder Karlssen might become Peter Carlson. You would need to know the new name.
It is the same for naturalization records. You would need to know when they arrived in the USA and where they were living when they applied.
Most states in the USA do not make birth records available to the public untill 100 years after the birth. If you know the name of the person and the place and date, and can prove your relationship, most states will send you a copy of death and marriage records. Unless they know that the person is dead, most states will not release a copy of a birth certificate to anyone not named on that birth certificate (i. e. the child or his parents).
Please let me know if you have questions.
All the best,
Is it not enough to know the names, when they are born ?