I think I way over-analyzed this. The easiest way to do what I want is with a simple MapThread:

Ns = {"Co60", "Co61", "Co62", "Co63"};
(*Set the array of constants up*)
\[CapitalGamma]Vals = 
 MapThread[ToExpression[StringJoin[{"\[CapitalGamma]", #1}]] &, {Ns}]
(*Set them all to 0*)
MapThread[{#1 = 0} &, {\[CapitalGamma]Vals}]
(*Define the useful constants*)
\[CapitalGamma]Co60 = 20

But I can see how it would be useful to use indexed variables here. It certainly looks quite a bit cleaner:

indexedVariable[var_, indicesValues__] := 
  With[{dict = List[indicesValues]}, 
   Scan[(var[#[[1]]] = #[[2]]) &, dict]];

indexedVariable[dict, MapThread[{#1, 0} &, {Ns}]]

Thanks for the suggestion!

Programmatically generating variable names is almost never a good idea in basically any language. The function "ToExpression" and its cousins in other programming languages (usually called eval or something similar) are the source of many sins and much suffering. If you find yourself using it, you likely want to restructure how you are approaching the problem.

1. You want to use a list to store the values. Instead of:

   example1 = 0; example2 = 0; example 3 = 1; example4 = 0;

Use:

example = {0, 0, 1, 0};

The values can be accessed as:

example[[1]], example[[2]] ....

1. If most of the values of your list are zero, use SparseArray:

http://reference.wolfram.com/language/ref/SparseArray.html?q=SparseArray