These two functions create anchor links, and you can customize a lot of it, but it's impossible to add a class through just using their parameters alone. Use the themes functions.php file to give these links a classname:
add_filter('next_posts_link_attributes', 'posts_link_attributes');
add_filter('previous_posts_link_attributes', 'posts_link_attributes');
function posts_link_attributes() {
return 'class="styled-button"';
}