I’ve got a fairly vigorous blackberry garden that I started three years ago. I’m digging out another as soon as I can this spring. I live in central Kentucky and have silt loam soil, so YMMV.
Assuming that you haven’t started the garden yet, what I would do is (after the ground has thawed, of course) completely dig out the area where you are going to plant the blackberries, setting the soil aside. Blackberries have fairly shallow roots, but you’ll still want to dig to a depth of a foot or so. Fill the pit half way full with peat moss, which should be available at your local megamart like Lowes or Home Depot. Gradually mix your soil back in a shovelfull at a time until you’ve got a full pit full of well-mixed soil. Actually, keep it up until the pit is raised a bit; it’ll settle quite a bit later. The blackberries will thrive in the organic soil, and the pH will be exactly where you want it. If you can, you’ll want to keep the berries mulched every year with pine straw, which will also keep the soil pH nice and low and continue to contribute organic matter to the soil.
If you want to stay on the organic path, add bone meal (heck, add it anyway) which will provide plenty of phosphorous and a bit of nitrogen. If you don’t mind chemical fertilizer, Muracid (as noted) or anything advertised as “good for azaleas” works great. I’d avoid adding sulfur if you haven’t had much experience with it–it’s easy to add to much and burn your plants, especially if yo have new transplants.