I like the shape of the annie bags including
http://www.byannie.com/carry-on-travel-bag which is the same size as the ones GEMRM posted. I see that they are 18½" long x 13¾"H x 8"D. I'm thinking that another possibility would be something like
http://www.sylviasstitches.com/2016/...case-tote.html might work with a recessed zipper (can use search for "add a recessed zipper to tote instructions").
I found a bag at thrift store that I was able to fit my Tiny Serger in. Actually, it is a little on the tall side with the handle folded down but fits well with the controller and power cord on one end. The dimensions are approximately 13" W/long x 9" H x 6" D.
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Not the best pictures, but might give you an idea of type of bag and how the Tiny Serger fits. The bag has webbing all the way around even the bottom. It is unlined heavy nylon canvas, I think. It reminds me of a zippered sofa cushion cover, but with exposed zipper instead of lapped zipper. The front, bottom and back are one piece, much like the FW tote above. The sides and top would be 4 pieces. Two would have the zipper centered on it and the finished width would be the size of the lower ends of the sides. Something similar to the instructions found at
https://www.onlinefabricstore.net/ma...with-a-zipper/
Janey - Neat people never make the exciting discoveries I do.