I've always found it hard to register the two colours when printing (to get the second layer to fit in the right place on top of the first colour) although the two pieces of lino are similar shapes. So I tried gluing the lino blocks onto pieces of wood the same size, and putting a pencil dot at the corner of the block (on the fabric) each time I printed, to try and line up the second block in exactly the right place on top of where the first had printed. But that didn't work - the two prints were often still offset.
So I decided to make up a screen with the same design, to see if that was easier to register...
I made two screens on mesh stretched in embroidery hoops, and painted with screen drawing fluid then coated with screen filler. When they were dry, I washed out the drawing fluid under the tap.
Then I printed the first layer using fabric paint and a plastic card to spread the ink. That printed fine.
Then the second layer, placing the outlines of the berry shapes by eye on top of the blue dots of the berries, by looking through the holes in the screen and wiping the screen with a cloth in-between each print.
It did work. The outlines of the berries are a bit thick - this was ok in the lino prints but looks a bit crude somehow with the screen print. I could paint the second design on a screen again, with a finer paintbrush, but at least this way I was able to register the outline (pink) on top of the blob-shaped berries (blue).