You should always report all income filed with the IRS (i.e., all 1099s) on your return. (The IRS does have a matching program to ensure that all 1099s reported to them are included on the recipient's income tax returns. ) This does not mean that you will have to pay tax on the same income twice (see below).
After you have recorded both 1099s in the income section of your schedule C, you are going to back one of them out by treating it as an expense.
In the Expenses portion of your Schedule C (Self-employed profit or loss), you should add Other miscellaneous expenses. For the description, put in "1099 income reported twice" and then enter the amount of the duplicate income.
