Well, here's something from someone's blog that recommends a tool I used to use for everything. (see link attached at the bottom of message)

You can also get a food mill, which is referenced on the same blog.

I bought a Squeeze-O at a garage sale and I love it, but they don't make it under that brand anymore. I think the Victorio is the same equipment under a different name. Paste this link into your browser http://www.preparedpantry.com/victorio-strainers-food-mills-accessories-canning-supplies-potato-ricers.aspx

You might check eBay and get a good price on a Squeeze-O or a Victorio. Mine has three screen tubes. I've used it for berries, tomatoes and for sand plums. It's a great tool to have if you process berries every year. Cleans up really fast, doesn't make a mess, processes a lot or a little in pretty short order. --Ilene

Here is a link that might be useful: cone sieve

wow, i have a couple of those laying around. I didn't know they would take seeds out of blackberrys though. I'll have to try it.

I think they might work better if you cook the blackberries a little. Put them in a pot, kind of push down on them with a potato masher or something to release some of the juice, then cook on low, stirring occasionally, till they've softened up a bit.

You can do it without cooking first but it's easier this way. --Ilene