I want a drone, using only acoustic instruments, with as little effort as possible, to accompany singing.
Trivially every wind instrument with a reservoir, like bagpipes, harmoniums, organs. When the player's mouth cavity is the reservoir, this is called "circular breathing" and can be used for wind instruments with little air use. The didgeridoo is regularly played in that manner, but circular breathing is also an advanced technique in some demand at professional level for instruments such as oboe and flute.
Then there are instruments with a continuous tone even if not of indeterminate length, like bowed strings. The hurdygurdy even gives arbitrary-length notes by employing a circular bow and a crank.
Then there are instruments that are kept vibrating mechanically continuously, like singing glasses or even the glass harmonica, or percussion instruments played with soft mallets in a roll, like cymbals or timpani. There are even plucked string instruments commonly played in a semicontinuous technique like mandolins and balalaikas.
Instrument sections with limited tone length can deliver drones by unsynchronizing breaks in their tone.
Organ, bagpipe, wind gong/tamtam, bells (including church bells as well as plate and tubular bells), Hurdy-Gurdy
The pipe organ is obviously the acoustic drone instrument, as with a single keypress it can sound for ever. And even when the key is released the sound will continue, thanks to the long reverb in churches