Minecraft: How to make "unenchantable" items?

You can, in at least some capacity, achieve this.

Assuming that your player cannot gain access to another tool identical to that one (but no enchants), then all you need to do is wear down the tool multiple times, repairing it each time in an anvil. Each time you repair it in the anvil, it will cost more and more xp until eventually the item becomes "Too Expensive!". Then, unless they go into creative, they will not be able to add any more enchants to the tool, however:

• They will not be able to repair it in the anvil anymore
• They CAN still rename it
• If they repair it using a crafting inventory (by placing 2 of the same tool in it) this will reset the "Too Expensive!" limit (but will remove all enchants.