If your character is the Green Knight, you might consider a coat of arms that includes attributes that signify what the Green Knight represents. The Green Knight has often been compared to the figure of the "Green Man" which has roots in ancient Pagan culture as well as similar symbols in the older civilizations of the Middle East. The Green Man represented nature (trees, grass, etc.) and in keeping with the figure in Sir Gawain and the Green Knight, regeneration is a particularly important theme. Those are some things to consider: vegetation, the color green, nature (trees), regeneration.
The color gold is also significant because it is associated with Sir Bertilak and his wife. (Sir Bertilak is the Green Knight).
In general, the Green Knight represents a challenge for Gawain: a test of Gawain's loyalty. If Gawain had been pure of heart (honest), he would have given Bertilak the life-saving belt during their agreed exchange (following Bertilak's last hunt). Since the test involved an axe and the heart symbolizes purity and loyalty, these are two symbols which reflect associations with the Green Knight: axe and the heart. Any visual imagery for a shield might reflect this duality: loyalty versus survival.
As for a motto, for the Green Knight, the symbols are nature, regeneration, green, loyalty, and a challenge of conscience. The Norton version of this poem ends with the quote: "Hony Soyt Qui Mal Pense" which means "Shame be to the man who has evil in his mind." If you interpret the Green Knight to represent a challenge to a knight's conscience, this quote is a fitting motto. On the other hand, consider creating a new motto based on these ideas. If you want to stick with Latin phrases, search for those that speak of "honor" and/or "loyalty" and/or "nature."
You might consider duplicating Gawain's shield emblem, which is a pentangle, a five-pointed star, with the Latin motto Quinque virtutes, una culpa, loosely translated as "Five virtues, one fault or sin."
One of the important themes of Sir Gawain and the Green Knight is Gawain's perfect behavior as a knight (and knightly behavior, in general). His entire journey to find the Green Knight, including the temptations he faces at Bercilak's court from Lady Bercilak, which he manages to avoid while not violating his obligation to be polite, is one of hardship and loneliness:
Except for his horse, he had no company in the forest and hills/during this journey only Christ to talk to (ll. 695-96)
The Pearl-Poet is constantly reminding the reader of Gawain's virtues in the face of adverse terrain and events and, more important, that Gawain is intensely devoted to Christ and looks to Christ for solace in the face of adversity, as one expects of a perfect Christian knight of Arthur's court.
Because Gawain's virtues are always in groups of five, represented by the Pentangle on his shield (e. g., the five wounds of Christ, Gawain's five knightly virtues), using a motto that acknowledges the significance of five makes sense. More important, because Gawain has only one failure--his lack of confidence in his own virtues, expressed by his use of the garter from Lady Bercilak--a reference to that failure brings attention to one of the most important themes in the poem--the momentary failure of belief.
Thanks...now I need to quote from Green Knight. I am looking for where it says that the Green Knight comes in peace, but Arthur's men challenge him.
I cant find the lines. Do you know which lines it says this?
That is great, but my character is the Green Knight......so I need something focussed around him.