If you're thinking about the type of ship:
* Yacht: A smaller, more luxurious pleasure craft.
* Freighter: A large cargo ship.
* Tanker: A ship designed to transport liquids in bulk.
* Battleship: A large, heavily armed warship.
* Rowboat: A small boat propelled by oars.
If you're thinking about the act of scooping:
* Pouring: The opposite of scooping something out of a container.
* Dispensing: Releasing something from a container, often in a controlled way.
If you're using "schooner" in a figurative sense, meaning "a large amount":
* A little: A small amount.
* A bit: A small quantity.
* A trickle: A very small flow.
Ultimately, the best antonym for "schooner" will depend on the specific context of your usage.