good idea

I have found Papyrus Cards to be pretty helpful in mending or improving relationships. They do not always work, but they do work most of the time. the art is good, non-corny, and they have a lot of blank cards without messages. Here are some examples:
Feather Butterfly - Blank Inside - Greeting Cards

Couture Die-Cut Purse with Charm - Blank Inside - Greeting Cards

Western Style Flowers - Blank Inside - Greeting Cards

I buy them at Target where they are much cheaper than online (these online prices are a bit appalling, tbh).

Spend some time selecting a card that would mean something to her. Draw your own if have enough talent.

Write something along the lines of what ImperfectMe suggested (which is pretty perfect actually):

"Sis, I realize must have been very hard for you hear what I said. I hope you will realize, in return, that was also very hard for me to decide to tell you. It was a difficult situation, and I hesitated to tell you, but after a careful consideration, I decided that it was my duty to tell you. I hope that you can see it. THEN MENTION SOME GOOD THINGS YOU SHARED AS CHILDREN, WAY BEFORE YOU STARTED DATING MEN. I really hope that you and I will... EXPRESS YOUR HOPES."