The idea of denomination-specific tartans is rather new. After all, there really were no such thing as a "religious tartan" in the past. Tartans were worn to show clan affiliation, or district affiliation, etc. Not one's faith. Even the Clergy tartan was worn as an occupational tartan, not a "religious" tartan.

That being said, there have been some attempts to create tartans for various denominations.

An "Episcopal Clergy" tartan was "designed and copyrighted by Rev. John B. Pahls, 1966, to honor the clergy of the Scottish Episcopal church and of the Episcopal Church in the United States of America and to commemorate the bicentenary of the death of the Right Reverend Samuel Seabury, first American bishop" (from STA notes). Note that this is the Episcopal Clergy tartan, which really makes it still an occupational tartan, just more specific than the traditional clergy tartan. It's not a "tartan for all Episcopals."

In 2001 the House of Edgar designed a tartan for the Baptist Union of Scotland. This is not an occupational clergy tartan, but neither is it a tartan for "all Baptists." It is more specific to the BU of Scotland.

Now a couple of years later in 2005 the House of Edgar was commissioned to design a "Methodist Church" tartan. The STA notes on this one are scant, so I really can't say anything about why it was designed or for whom. It could have been designed for a specific Methodist church, or it could very well have been designed for the denomination as a whole. I really can't say. I'd suggest contacting House of Edgar for more details on that if anyone is interested.

Of course tartans have been designed for particular churches. Just a few I find in the ITI; Freemont Presbyterian Church, Trinity Presbyterian Church, New Providence Presbyterian Church. And you won't find it in the ITI just yet because I just designed it, but there is a new one for the Barbecue Presbyterian Church of Sanford, NC, for their 250th anniversary.

But as far as I know there has never been an attempt to design a tartan for the Presbyterian denomination as a whole.