How can I help my sister cope with her son's suicide?

I am sorry about your nephew's death. You may find it helpful to talk with a  counsellor or psychologist in your area who specialises in grief and bereavement.

As well as helping you with your experience of the loss of your nephew, they can perhaps provide you with some insight into how your sister may be responding and why. 

I guess moving forward with your sister feels difficult in light of the 5 year “silent treatment”. One way to approach this would be to tell her exactly what you've told us: “I don't know if you'll accept this coming from me, but I want you to know that i love you and am sorry you lost your son. Please let me know if I can do anything for you. I'd really like to put the past behind us. You're too important to me for me to hold on to old grudges.” Something like that - you will find your own words, but can you see what I'm trying to express? It's about you loving your sister and feeling sorrow for what she is going through.

Perhaps your feelings towards your sister are mixed - like anger over past resentments combined with the empathy I'm talking about? She may be feeling something similar and in that case, the first response you receive may be an angry one “You don't understand! Stop pretending you care just to make yourself feel good.” In that case you will need to practise patience and stick to your message of love and compassion.

This is easier if you have been practising it with yourself. I'm specifically referring to the need to forgive yourself for blocking your sister out and also to forgiving her for whatever prompted that behaviour. When you forgive her, you will free yourself. But those are just words, so don't take my word for it. Do it and see if that is what happens. What do you have to lose that you haven't lost already?

I think that Julian has offered you some excellent thoughts.

One other one (assuming that you and your sister live in the same area):

Maybe rock up to her house with some (preferably home-cooked) food.

She will have a lot to process right now and organising meals is probably low on her list.

Bringing her and her family some home-cooked food is non-judgemental practical help which shows that you care about her.

OH I am so sorry to hear of all that you and your sister are going through. Death is hard enough and losing a child even more so. It reverses the natural order of things and is every parents worst nightmare. But when it is compounded by suicide it is even more difficult. 
Given the past difficulties you have had with your sister it is understandable that you are at a loss as to how best to help her. We cannot presume to know what she wants or needs right now. Perhaps the best thing you can do is to let her know that you are there for her in whatever way she needs. Come forward now, show up for her and be available. Then the rest is up to her. Grief is so individual and each person responds differently. She may want to talk or not. She may not know what she wants and what she wants may vary from moment to moment. Be generous in your understanding and remain steadfast in your intention to be loving and compassionate. Hold her in your thoughts, and take your cues from her, after you have told her that you love her and that you are there for her. It might be the best you can do right now simply to let her know you love her. All the best.

I meant to add, you can find loss and grief counsellors through the National Association for Loss & Grief. They have branches in most states I think.

If you're in NSW: http://www.nalag.org.au
or Victoria: http://www.nalagvic.org.au

As well as the many excellent suggestions offered by other counsellors, it seems to me that you have also experienced enormous losses - not only the deaths of your nephew and sister's grandchild, but also the loss of relationship with your sister. You may consider looking at counselling for yourself, to process your own grief and loss, and perhaps gain some different perspectives about how your sister's ways of coping may have affected your relationship with her. It can be difficult to understand and come to terms with a famiily member's decision to push others away as a way of coping with difficulties, especially if your way of coping is to reach out and connect. If your sister is not willing or able to connect with you at this time, it's vital that you get the support you need. Take great care of yourself.

So sorry for your loss. At this stage I would think that just being available to listen and care is all that is required. If she rejects your care let her do that, it is up to her. Look after your sister the best way you can as she struggles with her loss. Don't forget to look after yourself also.

I think that simply letting your sister know you are thinking of her and there for her is all you can do at the moment. Consider what supports your sister has now, apart from you. She may be more inclined at this point in time to rely on those supports given that you have not spoken to her for so long. Is there a way in which you can send a non-intrusive simple message of support to her by letter, email, phone call or intermediary?