What can I replace copper with?
What you need to look for is two metals with a large "Galvanic Potential" between them. This is also known as a metals Anodic Index. Copper and Zinc is just one of many options.

The following is a partial chart of Anodic Indices of various materials:


Image source here.

As you can see, Copper is quite Cathodic at \$-0.35\mathrm{V}\$, while Zinc is quite Anodic at \$-1.25\mathrm{V}\$. You would expect a terminal voltage of about:

$$V=V_{Cu}-V_{Zn}=(-0.35)-(-1.25)=0.9\mathrm{V}$$

To replace Copper and get a similar voltage, you could use something like Nickel which is similar to copper at \$-0.3\mathrm{V}\$. Gunmetal (Red Brass) would also work, giving a similar potential to copper. Alternatively you could use something like Graphite - like from a pencil - which is at \$0.3\mathrm{V}\$, so would actually give you a much higher voltage.

Basically pick two materials, one which is Cathodic, and one which is Anodic.