Re: Barbara Ainsworth Montgomery's post pointing you to Martha Ainsworth's website - That is an excellent suggestion, a website I discovered a few years ago. While you are there, visit the companion page: http://www.metanoia.org/ainsworthhttp://www.metanoia.org/ainsworth and follow the links there for a lot of generic information concerning the history and origin of the AINSWORTH name.
That site explains how to order from THE SHAMBLES, OXFORD, ENGLAND. I ordered several items in person while visiting Oxford. This included the coats of arms and the wooden "shield" version. They had to be shipped later, of course. They do quality work and everything arrived in good order. I highly recommend them for this type material.
A word about "The Ainsworth Coat of Arms." There is no such thing as a FAMILY coat of arms as such. A coat of arms, in European heraldry, applies to a single INDIVIDUAL.
Also, a "generic" Ainsworth coat of arms (or any other name) is usually copyrighted and protected the same as other intellectual property, so it should never be used in a commercial way without explicit arrangements with the copyright owner. (I am not an attorney, only passing on what the heraldry books say)