Is there a good way to copy text within parentheses in Vim?
Use text objects:
yi( (or ya( if you want to include the parenthesis).
You can also use " to work inside quotes, etc. See the link for details, or type :help text-objects in Vim.
A slightly shorter alternative to yi( is yib. Similarly yiB is equivalent to yi{ - yanks the contents inside braces.
Personally I usually do vib (visual select the text inside braces) first to make sure that the expected text is selected, followed by a y.
For more text object goodness, see :help text-objects.