Which template is it?
 

What template would I have to modify to insert text under each product page?

I would like it to display right under the quantity dropdown list. I've tried product.tpl and products.tpl

That is the product.tpl template. Look for this line of code:

<FONT class="ProductDetailsTitle">1</FONT><INPUT type="hidden" name="amount" value="1"> {$lng.txt_product_downloadable}
{/if}
{/if}

Insert your text after the last {/if} tag and you will see it show up between the quantity drop down and the add to cart button.

Is the only product.tpl file in the main folder? I can't find the text your specified