Im assuming you mean Chinese dumplings. How about just some plain steamed or sauteed Chinese greens (gai lan or garlic stems or similar) lightly drizzled with fish sauce and topped with fried shallots?
Also some thinly shaved, homemade pickled vegetables are lovely with Chinese dumplings.
You could also get some seaweed and a Japanese style salad with the amazing carrot and ginger dressing.
I assume your dumplings are Chinese but Japanese have them tot so why not mix it up a bit.
Even go with the Bento box concept - a little bit of everything