The Diogennia is the celebration of Zeus' birth. The date is a bit hard to fix, as it was observed at different times in different regions. There are, in fact, two main tales of His birth, the Cretan and the Arcadian, not to mention several variations on how He was raised thereafter and by whom.
In modern times, specifically at the Hellenic Temple of Apollon, Zeus, and Pan, we tend to observe His birth not long after the Kheimonia or Winter Festival and before the Theogamia/Gamelia.
Appropriate offerings include amber incense (always good for any offering to Zeus), candles and/or golden bowls to recall the light in the cave on Crete where He was born in one of the primary myths, and crowns in honor of His position as King of the Gods. Honey features prominently in food offerings, relating to the light in the cave as well. If you are more drawn to honor the Arcadian myth, offerings related to wolves would be appropriate, as He was worshipped there as Zeus Lykaios.