To me the jar is a bit of sympathetic magic. You put into it items that symbolize what you’d like to have in your house (health, wealth, peace, etc.) then dedicate it to Zeus, who oversees everything, in his domestic aspect. The other household gods can be represented in it too like cinnamon for Hermes, Bay for Apollo, garlic for Hekate etc. The idea of the jar itself never made sense to me until this occurred to me.
“Put the lid on a new two-eared Kadiskos, crown the ears with white wool and let down the ends of…the thread from the right shoulder and the forehead and place in it whatever you can find and pour into it ambrosia. Now ambrosia is pure water, olive oil and pankarpia. Pour in these.” – Exegetikon of Antikleides
Pankarpia (all fruits) is a mixture of several kinds of fruit offered to the dead on the third day, Chytroi, of the Anthesteria. In Christian Byzantium, panskarpia became the offering of kollyba (kolyva, koliva, kollyva and kolliva), a dish of boiled wheat, which was distributed to the congregation for memorials. Various ingredients are added to the kollyba such as sugar or honey, barley, rice, oats, buckwheat, pomegranate seeds, sesame seeds, poppy seeds, raisins, figs, dates, parsley, mint, cinnamon and nuts.
Seems to me the time to renew the jar offerings would be during the spring or fall. In the spring, it would be in hope of the harvest to come. In the fall it would be thanks for the harvest and may it last until spring. So a good time to do this would be the Diasia (roughly spring equinox) and the Pompaia (roughly fall equinox).
What I did is pull out my metaphysical book on plant symbolism and added items to the jar that I wanted for my family and my home.
Pecan – to maintain employment
Lemon juice – promote friendships
Rose – love, protection, luck
Marjoram – happiness, love, health, money
Clove – prevent gossip, protection, money
Olive Oil – peace, protection
Oak/acorn – Zeus symbol, health, luck, money
Cinnamon – spirituality, success
Barley – keeps evil and negativity away
Cumin – theft protection
Honey – for sweetness
Water – life’s necessity
My current jar is just a corked bottle but I plan to used a glass canning jar with the attached lid and rubber gasket in the fall when I renew it. Mine sits on a tiny shelf in my pantry. I’m still looking for a snake charm to tie onto the jar.