I am assuming the web  part that you have created is reading from custom
list.

customize the web part  the way you want it. Save it as a template (STS
file). Import that template in site  Template Gallery. Now you can see the
template in any site (or area) created under the site where you imported it.

With what Bill have described about the data tunnel, it should yield the
desired results.

PS: Using FP you can create a data source pointing to the web part list  in
catalog and can get the same results.

Let me know if this solved your problem.