This all depends on your SIL's personality. I just had my 2nd miscarriage. I had my first the spring of 2005 - had a healthy baby 6/06. We started to try for #2 and had a D&C the day after Christmas 2008. They don't know why - apparently lots of pregnancies end in miscarriage when it's not viable and the body knows. So, I kind of know how she feels - but for me - I'm really ok. I had my moments - but it's not hitting me that hard (maybe it would if God forbid I do get to 3!)
Now, if it were someone else I know - she would view it as a failure and a weakness of hers. She'd be ok around everyone else, but not at home. Chances are, if your SIL is holding it in and her husband (I assume this is your husband's sister) is the one who sees it all at home - she views it as a weakness and will not be open to talking to anyone outside the confines of her home (if she is even willing to talk about it there).
In that instance - you need to be gentle. You can open a conversation with 'I' statements, "I would feel...", " I can only imagine..." and those kinds of things. If you bring up that her husband asked you to talk to her - it may make her deck of cards fall and backfire on you both.
My suggestion is that you be there for her - by calling and taking time to be with her. Absolutely be open to the conversation about the miscarriage and even bring it up once or twice, but when (b/c it's likely NOT an 'if') she doesn't want to talk about it with you - you can't push it.
My other suggestion is to tell him to be the heavy and take her to counseling - either by herself or together. One way to do it is to say something like "I know you don't want to talk about this stuff (or I know you feel ok with all of this), but I am having a hard time dealing with my feelings and I want to be there to support you and be there for you and I don't know how. I would like someone to help me be a better person for you and our family, but I can't do it alone b/c it involves both of us." Basically, asking her to go to therapy but taking all the responsibility so she doesn't feel like she's being asked to go in order to be told all the things she's doing wrong. Chances are, as long as the therapist is good - she'll begin to open up more.
Good luck - it's hard when someone is having such a hard time. I hope that helped.