Caribbean is not the theme – that is the colour overlay you are using. But that does not really matter.
Using the theme editor panel you need to open the theme CSS file which – if using ‘default’ is called ‘default.php’. Look for the entries for:
#spMainContainer a.spButton – and for #spMainContainer a.spButton:hover – which are the two entries you probably want to look at for changing button styling. Make a note of the items you plan to change – i.e., ‘background’, ‘color’ – you want the name of the variable in the php echo statement.
When you have noted those – open the ‘caribbean’ colour overlay file and look for the variable names you want to change and make your changes accordingly. Follow the same pattern as other entries in that file. As easy as that!
Such changes to a supplied theme/overlay will get overwritten if you then update that theme from us so as always we recommend that you create your own SP theme so that any customisation is not lost during a future update. (http://codex.simple-press.com/codex/themes/theme-basics/creating-a-theme/). This is also an easy and simple process.