I have made Elderberry jam. First off, I think there are a couple kinds of elderberries, black and red. The red are not very good to eat. I would think that to make syrup you would cook the berries with a bit of water, much like you would for jam. This makes a very nice bunch of juice. Then strain it through a cloth to get the seeds and skins out. ( I skipped this part to make jam). Then I'd just add enough sugar to make it a syrup and cook it to the desired thickness. (not too much, or you'll get jelly) Then process it. I know this isn't an exact recipe, but I'm sure there is room for a little experimentation here. My mother used to make Jam, and also wine from these. Makes good wine!