There are a few ways to do this, depending on how your site's theme is set up. If the second gallery is on a page with a different page type, then I'd change the page type template to add an additional css class to one of the container divs.
If, on the other hand, the galleries are on pages that share the same page type, your best bet is probably to create a custom template for the Gallery:

1) Create a new directory on your server here:


2) Copy this file:

...to that new directory you created, and rename it to something else (I'm just making up the words "alternate style" here, but you can call it whatever you want):


2b) Also copy this file:

...to here:

(this step has nothing to do with what you want to achieve -- it's just to prevent a Concrete5 bug from happening where it looks for that css file in the wrong place)

3) Change the CSS class of the outer div in that file (should be around line #9) from this:

...to something like this:


4) Now put a different style for that ".deluxe_image_gallery_container_alternate_style" (or whatever you called it) in your theme's CSS file.

5) To activate this custom template for the gallery, go to the page with the block on it, go into edit mode, click on the gallery block, and choose "Custom Templates" from the popup menu. Then choose "Alternate Style" (or whatever you called it) from the dropdown menu, and click the "Update" button.

Hope that helps!

-Jordan