Determining Correct date to record refund

Your last sentence is correct. You issue the refund as a customer credit memo, which reduces your 2019 income and puts the amount on the books as an other current asset. 

Open the c.m. and there will or should be an option to issue refund. Do that with the January 2020 date

Customer>New Transaction>Credit Memo

Use same account as original sale, or any appropriate expense account. This refund is expense or contra-income.

The procedure is exactly the same for cash accounting, only the reporting is different. Under cash rules the change to net income does not happen until january

I am not sure I fully understand. I have included the timeline below along with the journal entries.

1) Customer buys item on credit and a third party will do a bank transfer to pay for it.

12/1/19          Accounts Receivable                    $1,000

                                      Sales                                                                 $1,000

2) I receive the bank transfer from the third party.

12/10/19       Cash                                                $1,000

                                     Accounts Receivable                                     $1,000

3) I approve a refund to the customer and am waiting for the third party to do another bank transfer to credit my bank account. The journal entry credit account is what I am not 100% sure about. I am leaning towards crediting the liability account below, but when I enter a credit memo, it credits my accounts receivable account instead. This would make sense if I was simply using this credit to lower their overall A/R balance due, but since they have no A/R balance due and the third party will be doing a bank transfer to credit my bank account, then I would think I would need to create a liability for this instead?

12/20/19       Sales Returns (Contra Revenue)  $1,000

                                      Refunds Payable (Liability)                        $1,000

Thanks!