I have Paypal standard. Is there a way to set up my account so that I can accept coupon/discount codes from customers during checkout (and it will automatically adjust the charges)?
At the present time, PayPal's Website Payments Standard does not have any built in features or options for supporting coupons and/or discounts from within your PayPal Account.
However, Website Payments Standard does have available several "discount" variables which can be implemented with your individual item button code. You can also combine these "discount" variables with some custom scripting to create discounts using "promo code" and/or coupons. See this page for tips and real world working examples.
In order to apply discounts and/or coupons to the entire shopping cart, you have two options. Use a 3rd party shopping cart or a custom developed mini-cart application. Both methods calculate the logic on your web page or web site first, then use the "upload" method to pass the end results to PayPal. You can find examples and tips concerning the use of the "upload" method here. Here's an example of a mini-cart. And you can find a list of third party shopping carts here. For example, this cart is easy to get up and running.