I am generally lazy and only want to knit the "front" side of any pillow, I always hand sew a fabric backing to the pillows. I have done one piece fabric backs but they aren't the best choice. Pillows get dirty and need laundering. With a one piece back, the inside of the pillow has to be washed at the same time as the pillow case. A better choice and my favorite method of backing a knit pillow is to make a two piece flapped backing of fabric which makes the pillow form inside easy to remove and the pillowcase easy to launder.
Some of my knit pillows have been around our house for some time. The Field Of Diamonds Pillow was made many years ago and was featured in House and Garden Magazine in 2003 along with the Turkish Leaves Pillow. The photo is below.
Once I removed the worn backing, I chose some new backing fabric (not silk, but a durable cotton). Laying the pillow top down on a flat surface, I measured the pillow. You can see how the knit fabric has stretched over time so I measured the square edges.
Take the measurement and add 1" to the length and add 4" to the width of the measurement. Cut the fabric that size. I used a quilting graphed ruler - I love these tools. You can see the lines I drew with a Sharpie. Cut out the rectangle of fabric.
Fold the fabric in half with the shorter sides together. Cut the fabric in half.
Referring to the photo, press the 2 short sides and 1 long side under 1/2". At the remaining longer side of the piece, turn the edge under 1/4" and then 1/2" again. Repeat for the second piece.
Here is a close-up of the twice turned under edge. This will form the overlapping flap for the removable backing.
Using a sewing machine or by hand, stitch down the twice folded edge.
This is what the two pieces will look like when hemmed. They are ready to be attached to the knit pillow front.
Using straight pins, attach one of the pieces of hemmed fabric onto the pillow with wrong sides together. The double hemmed edge should be at the center of the pillow.
Using small whipstitches, sew the second piece of fabric to the knit pillow. Here is the pillow with both pieces attached before pressing.
Good as new. Quick to do and the pillow case can be removed quickly and laundered.