I bought Certificates of Deposit for my Children, with my name & theirs on the CD. The accounts show up on my 1099INT, but the interest is theirs. How do I report it?

If the social security number on the CD account is yours, you are considered the "owner" for income tax purposes.  You should have used the child's SSN if you intended the child to be the owner of the account.

Most account registered this way are joint tenants with right of survivorship, ie, it becomes the child's upon your death.