Storing a spell in the ring requires the use of a slot
From the description of the Ring of Spell Storing, this is not immediately obvious but it does state that:
The level of the slot used to cast the spell determines how much space it uses.
Fortunately, Jeremy Crawford has clarified this in a series of tweets:
Armando Doval @armando_doval
@JeremyECrawford can you cast a spell into a Ring of Spell Storing without expending a slot? Description seems to assume slot is used.
Jeremy Crawford @JeremyECrawford
Casting a spell into a ring of spell storing does require a spell slot. #DnD
AdventuresInLethargy @theactualevan
I guess ritual casting into a spell storing item is out too, then?
Jeremy Crawford @JeremyECrawford
Correct
Uri-AHH! @Panoramic_Panda
Can you cast a spell into a Ring of Spell Storing from a wand?
Jeremy Crawford @JeremyECrawford
It requires a spell slot. A wand doesn't expend a spell slot.
So this means that any method that does not use a spell slot can't be used to store spells in a ring of spell storing.