The shield guardian amulet's rarity is "unique" (without a certificate)
The amulet is unique
The D&D Adventurers League Frequently Asked Questions document says:
Any item that doesn’t have a complete description (e.g., shield
guardian amulet, etc.) is considered unique unless you have a
certificate which establishes the item’s rarity. [...]
Without such a certificate, its rarity is unique. (DDALFAQ v7.1 p. 9)
Note that the FAQ specifically calls out the shield guardian amulet as an item without a complete description which is considered unique. But even without the specific call-out, the rules would still categorize it as unique:
Unique is a specific rarity category. Any item not described in the DMG that doesn’t otherwise have a listed rarity is considered unique.
There is no rarity listed in the adventure treasure block1 or the Monster Manual Shield Guardian entry (MM p.271). There is no mention of the item in the DMG or Basic Rules at all.2
Since the item's rarity is not specified in any printed material, the shield guardian amulet must be considered an unique item per DDAL rules.
Unique items cannot be traded
The Adventurers League Player’s Guide says:
Items without a specified rarity are unique, and
can’t be traded. (ALPG v7.0 p. 4)
and the DDALFAQ also says:
You don’t need a magic item certificate if you wish to trade your permanent magic items unless the item’s rarity isn’t described in the print-version of the resource it’s found in. If this is the case, the item is unique and can’t be traded. (DDALFAQ v7.1 p. 8)
Thus, the shield guardian amulet cannot be legally traded in DDAL without a certificate.
Note about certificates
Certificates have been released for the shield guardian amulet in previous DDAL seasons.3 However, note:
The item to be traded must be found in the
adventure listed on the certificate. You can’t—for
example—use a certificate for a shield guardian
amulet from Out of the Abyss to trade a shield
guardian amulet found in Curse of Strahd. (DDALFAQ v7.1 p. 9)
1 - Spoilers for particular adventure and plot points:
Treasure. The queen wears a bronze and adamantine medallion that has the word "Vorn" etched into it. This is the control amulet for a shield guardian (see "Vorn," page 83). None of the goblins have any notion the amulet is related to the object they venerate as a minor deity. (Tomb of Annihilation p. 90)
2 - Though interestingly it is listed on D&D Beyond as the Master's Amulet, a wondrous item with a rarity of "rare". This is curious since it is not actually listed in any printed source. However, the provenance of this item being added is a bit suspect. Regardless, the DDAL rules (mentioned above) should supersede it.
3 - It is interesting to note that this certificate does verify that the item is considered to be a magical item at least according to the DDAL.