Can my 16-year-old make a Roth IRA contribution

Age is not a determining factor. As long as your child has earned income with which to open the Roth IRA account, and as long as he or she falls under the adjusted-gross-income limitations, then he or she can make an IRA contribution regardless of age. The key is having earned income, such as from working a job. See more on this point a few questions down.