To journalize the entry:

Paying for merchandise previously recorded on credit (accounts payable) with a discount.

Obviously cash is credit for the amount paid.

However, the merchandise inventory account is credited for the full amount of the invoice.

Where does the "sales discount" amount go if there is not a "sales discount earned" account?

Would this be 2 journal transactions? One for the amount paid and one for the discount amount? And still yet where would the discount amount go?

The situation you are describing is a Purchase.
The journal entry to record the purchase is:
Debit Purchases for the amount
Credit Accounts Payable for the amount

If you make a payment within the discount period and are using the Gross Method then the journal entry is:
Debit Accounts Payable for the total amount
Credit Purchase Discounts for the amount of the discount
Credit Cash for the amount paid

If you use the Net method you record the purchase with the discount taken. For example if you made a purchase that costs $20,000 terms 2/10, n/30.
The journal entry to record this is
Debit purcahses for 19,600
Credit Accounts payable for 19,600

The journal entry to record payment within discount period is:
Debit Accounts Payable for 19,600
Credit Cash 19,600

If the payment was after the discount period then the journal entry is:
Debit accounts Payable for 19,600
Debit Interest Expense fro 400
Credit Cash for 20,000