My son has income earned doing research from the National Institutes of Health, for which he received a Form 1099-G. Can he make an IRA contribution?

Probably not. An IRA contribution can be based only on earned income. A fellowship or grant type of payment is different from income for services provided. Grant recipients at the NIH are not considered to be providing services, so the funds are not considered to be earned income. There are some earned income exceptions for making IRA contributions, but an NIH grant is not one of them.