If you are using an actual font, then something like text-shadow: 2px 2px 2px #000; is worth a try. But otherwise, if it ha to be an image, I'd say you are better off creating the drop shadow in a graphics program.
Not necessarily text, that was just an example.
And yeah I thought of that adding the shadow to the image
but was hoping for a code option to have the flexibility of
changing the background colours in future edits
O well, if it's easy to design then do it yourself! Luckily for Adobe, Photoshop doesn't have to be able to run in a wide range of faulty browsers! Some browsers can't even get basic CSS to work properly, so more complex things like this are pretty much a pipe dream, it would seem. At least, we'll be getting pretty old when CSS and browser support offer anything like the functionality of Photoshop. Unless online applications kick off in a big way and leave html and css behind.