Sweeps were often stored in the waist like spare yards. Like things in the age of sail, there may have been alternative methods.
I have not seen photos of contemporary models showing the sweeps, but the below from Preble Hall has two spare yards where the sweeps possibly were also stored. They would be up and out of the way when not in use.
A very timely post, I’m presently working on the 16 sweeps for the Syren. When finished they will be stowed in bundles of eight on the gallows bitts each side of the longboat. See attached photo from the manual by Chuck Passaro.
Many thanks, guys. Those ideas work well on those ships. I didn't mention, not wanting to skew the results, but the ship in question is the bomb vessel Granado. She had no room on her decks for longboats nor spare spars and such. Luckily, she was usually accompanied by a tender, which could provide such items. Sweeps, however, would be clumsy and time-consuming to transfer, yet were instrumental in the operation of a bomb vessel, where a launch would normally set a kedge anchor near the shore attached the the bomb vessel, set the vessel some distance from shore, and use the sweeps to help position, aim and stabilize the vessel. Thus, sweeps were very often necessary to the ships operation, not just in calm water.
The photo below shows the cluttered decks of the Granado. It would seem that not even the mortars and 4" guns could be used at the same time, and anything on the already overcrowded main deck would severely hamper normal operations:

The only position on-deck I see for sweeps to be stored is on the quarterdeck, shown in red above. But even then they would interfere with the railing, completely block one at least one set of stairs (depending on if all 18 sweeps were stored on one side, or 9 on each), and possibly hamper operation of the tiller.
To me, the most reasonable place for storing them is extended outside the hull on some sort of rack, indicated by the red lines above.
The Granado at the Royal Museums Greenwich show some of the sweeps off the vessel for reference:

and also on the main deck, but occupying the space that most of the 4" guns would have been mounted:
Again, I believe the most reasonable place for storing them is extended outside the hull on some sort of rack. Someone here posted a model photo with some sort of rack (not the Granado), but I can't seem to find it.