I had the same problem, and the child theme didn’t work for me (Replete 1.0). It seems that Replete currently doesn’t support child themes.
So I changed line 160 in functions.php from
wp_register_style( 'avia-custom',get_template_directory_uri()."/css/custom.css", array(), '1', 'screen' );
wp_register_style( 'avia-custom',get_stylesheet_directory_uri()."/css/custom.css", array(), '1', 'screen' );
and put my styles into replete-child/css/custom.css.
I think all the wp_register_style() calls around line 160 should be changed from get_template_directory_uri() to get_stylesheet_directory_uri(), then we could override the styles. I didn’t look at the other register calls, maybe they should be changed as well.
Hope this helps!