It is widely held that there are no Goblinoid Mages because they cannot speak the Ancient Elvish language of Magic.  This is not true, though pronunciation issues and innate prejudice has limited the progress of many Goblin Mages.
Only the ‘Common’ Goblins seem to have the facility or ability to learn Arcane Magic.  However there are Shamans among the Haeb, Buge and even the Ogres who practice an odd mixture of Arcane, Divine and Natural Magic. 

Prior to its sack and destruction, (1,200+ years ago) the Goblin city Lildith was the center of Goblin Magic.   Most, if not all, of the Goblin Magic Users at that time were a product of the School of Lildith. Most of the major Goblin magical works were produced in Lildith.  The current school in Kassoh has never achieved the same level of power or accomplishment as was seen in Lildith. 

Goblin Magic ‘Items’

Much like human mages, Goblin mages were never invested in the enchantment of large amounts of armor and weapons that were not of immediate benefit to the Goblin Mages themselves.  Yes, they did enchant some weapons for their fighters and Goblin ‘Heroes.’  But they lacked the ability, or the desire, to produce powerful weapons and armor for the benefit of their non magic using brethren.   While enchanted ‘goblin tooth’ style swords and daggers were created and are still made to some small degree in Kassoh, enchanted armor, beyond shields and helmets, were, and are, virtually unknown.  In their place the Goblin Mages created a variety of protective devices akin to Rings and Cloaks of Protection, Bracers of Defense and similar items.  These could be usefully employed by the Mages themselves as well as their less talented allies. 

One common Goblin item, made then and now, are Enchanted Earrings.  Considering the size of Goblin ears, and their importance to their owner, this is hardly surprising in itself.  These come in a variety of shapes, sizes and functions.  Notably, wearing Goblin made enchanted earrings does not seem to impact on any enchanted finger rings worn, though there is a limit on how many enchanted earrings can be worn. (Two, one on each ear.)  It should be noted that while no self respecting Elf or Dwarf will ever be caught dead wearing or using Goblin made magic, many Goblin items do not work when handled or used by Elves or Dwarves.  In fact some demonstrate dangerous side effects and traits if so handled or used!  Perhaps as a reflection of the value of their human allies, most Goblin made items function perfectly well for humans and Halflings.

Another common, though by no means universal, feature of Goblin made magic is the widespread use of Bronze as the primary material of the item.  Where Dwarven and Elvish enchanters reached for steel, silver or gold, Goblin enchanters usually went with bronze. This is still generally true, though most of the various sized ‘Teeth’ made in the last millennia employ steel blades.