When you don’t know what else will work, simply send them a few of your hilarious pictures! Now is the time to bring out the hidden images of yourself, which you didn’t want anyone to see! Your partner won’t ignore picture messages, and will soon be laughing it all off. This is the best way to show that you don't mind taking the initiative.
Just remember that taking a little effort to make up after a fight is in no way giving up your opinions. It just means that you wish to make it work, and things like fights do not really matter.