I often shop with panniers: groceries, drinks, beer, even carried bouquet of flowers and potted plants, plus computer and bike parts, etc. If it fits in a shopping bag, it should be no problem putting it in a pannier. But the panniers should be strong and have stable and reliable attachment system. But my wife shops with cheap $25 Nashbar panniers just fine.
How exactly they're not working out for you? Too difficult to load/unload?
There are panniers made specifically for shopping, such as
Axiom shopper bags.