I echo what Forum Member X says - have a simple burial for bunny to say good bye. And then it's closed. If your child mentions it - fine. But don't bring it up again.
Your little fellow is WAY too young to be trusted with a small animal. No child under about 6 or 7 - and older for some - should ever, ever be left alone with a small animal. Impulse control is just not a feature in little children - and less so in some. You know your boy can be rough so he has an issue here.
I do not say this to rub your nose in this - but so often people think tiny children can do more than they should ever be expected to do. Even if your son was never rough with his sister, it is putting a huge burden on such a tiny child to give him responsibility which is too heavy to carry. I say all this gently though it might sound harsh. I do not blame you - but now you know.
I actually think the best thing would be to get a new bunny. In this way your son will not carry the doubt about himself in relation to an animal like this. And words are no good in such a situation - he has to experience that he can indeed be around - appropriately - small animals without harming them. He needs to feel carried by his parents so that he does not have to inappropriately rely on capacities which he cannot - and should not - have developed to ensure the animal's safety and his own behavior.
You must ensure that the rabbit's cage is such that your son can never get it out by himself - he must always ask. And do not expect that just because you tell him he must ask and he says yes that this has any bearing on his ability to do what he said - as a society we place way too much value on what comes out of a small child's mouth. We must instead hear and feel behind what a tiny one says and hold the space for him or her because they are not able to do so themselves - not yet. We must hear that by saying yes in such a situation that the child sincerely wants to do the right thing - like all little ones - but cannot yet. And that is where the parent steps in. It is unfair and totally out of touch with the realities of child development to expect that a little tiny child can monitor himself, has the awareness of self, ability to control impulses and self awareness to be able to do this - or that a small child in any way should have those capacities.
However, popular parenting advice is riddled with this kind of advice which goes by the Orwellian name of "gentle parenting". To my mind putting such a load on young children is anything but gentle.
So get that bunny and just take him out to play from time to time. While you hold him, say things like "what a soft and gentle bunny. See how we must stroke his fur like this? We must always be gentle with bunny." Let your son hold him if he asks - but only while sitting down so if bunny wriggles and your boy lets go - again, perfectly understandable - bunny won't have far to fall.
Your son might not want to touch the bunny. That's fine. Don't push. Just play with the animal yourself and if your boy comes to watch just murmur softly "hello bunny. This is your new home. We know how to be gentle and care for you." Your son might even come and hit the rabbit - this might be a way he is punishing himself for what he did - and a gesture of "help!" to you. Do NOT get emotional or alarmed if something like this occurs. Just stay centered and say "here, sweetie, this is how we pet the bunny" as if it never happened. Take your little boy's awful feelings about himself and what happened and transform them.
If your son says anything like "I killed the other bunny" you can say "Yes. That was sad. But now we will be able to care for this bunny and you will know how to be gentle with him." One doesn't want to cover up or pretend something didn't happen - but one also needs to take the emotion out of it (because such a young child can't) and transform it into a healing possibility. This rabbit remains in your protective sphere.
As for cutting its eyes open - very normal reaction. Don't buy into it - it is a way of covering up, perhaps his own attempt to push away the hurt. He might also know that this gets a rise out of you and does this to diffuse the situation - and of course all of this is absolutely unconscious. There is no "bad" or "good" here. You do what needs to be done - and never get into his stuff. If he cannot yet show the "right" emotional response, then you do it for him (whilst never pointing this out to him). There are many cases where children of this age seem to not react even to the death of a parent - please always remember that children of this age do not have a sense of "I" and therefore cannot be compassionate in the way which we adults might expect. By 7 or 8 he will be on the way.
Which doesn't mean that young children don't do things which look like compassion and even selflessness - but I would say that they are imitating. They are feeling and acting - but not out of self, rather out of what those around them do.