Member Card is an item in the “Event items” category (Key Items).
In-game descriptions
| Diamond / Pearl · Platinum · HeartGold / SoulSilver · Black / White · Black 2 / White 2 · X / Y · Sun / Moon · Ultra Sun / Ultra Moon · Let’s Go, Pikachu! / Let’s Go, Eevee! · Sword / Shield | A card needed for entering the inn in Canalave City. Oddly, the last date marked on it was 50 years ago. |
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Where to find it
Not placed on the atlas maps (so far: Red/Blue and Generation 3).
Sources : PokeAPI (items, item_flavor_text, machines) · atlas · pokeemerald species_info.h