Is there a simple method of tracking number of transactions sent to an address? I want to create a counter in my store displaying the number of units sold.

I'm not using a shopping cart, but simply placing a bitpay button.  I'm wondering if there is a way to query the blockchain, that will return the number of transactions sent to an address, over a given time period.
You can see the number of transactions for a Bitcoin address. That's easy. Either through a desktop wallet(Like Bitcoin QT) or using services like blockchain.info. Just search for an address there.

You can't do this for your site thought because you're using Bitpay and they provide a unique address for each payment to your site.

Even if you weren't using Bitpay, you would need to generate a unique address for each purchase on your site to be able to figure out which customer paid how much and when.

You could take an aggregate of the transactions and display them along with each unique address you used but I would strongly advise against it. Because then people could easily trace where you spend the Bitcoins that your customers paid you.

Try getting the number from your accounting records instead of trying to get it from Bitcoin payments ;)