How do I post a credit against a purchase order?

PO is never paid or not paid; it is a Tracking tool.

"However there is a smaller amount that I overpaid them on a past invoice."

Are you still carrying a negative AP from that? Or, did they issue a Credit to you later, and did you enter a Vendor Credit, so that you have this negative AP, now?

"How do I enter/reflect that in QB's to deduct the amount they owe me from the amount I currently owe them?"

You always enter In Full = capture the Total Cost for what you are buying, each time. You are asking about a reduced Net payout for Banking, not a reduction for this Purchase.

"Can and how would I reflect that on my bill when I send them payment?"

The Bill is what you owe as Gross.

How you answer the Prior Overpayment will drive how you are able to Use that previous overpayment against what you owe, now, to end with a Reduced payout, now. Example: In Pay Bills, you can Apply vendor Credits to open bills, even if you are not paying the bill at this time.

I am having similar issue with credits each month on my credit card.  Sometimes no charges for the month, but credits.  How to post this accurately?  
My reports are not reflecting correct figures when this happens.

Hello, @CindyMCA.

Let me guide you in recording the credit card credits you've received. This way, you can use it in paying your future bill.

1. Go to the Banking menu.
2. Choose Enter Credit Card Charges.
3. From the Credit Card drop-down, select the credit card account.
4. Select the Refund/Credit radio button.
5. Choose the appropriate Vendor name and enter the Date, Ref No, and Amount.
6. Enter an appropriate memo to describe the transaction.
7. If you returned Items, select the Item tab and enter the Items and Amounts from the refund.
8. If the refund does not have Items, select the Expenses tab, select the appropriate Accounts, and enter the Amount.
9. Click the Save & Close button.

You can browse this article to learn more about tracking the credits and refund you've received from a vendor: Record a vendor refund in QuickBooks Desktop.

Always feel free to visit us here in the Community if you have other questions about applying credit to your vendor payments. I’m always here to help.