I am looking to add a list webpart to a Subsite. The list is on the parent site. Any help is appreciated.
The List View Web Part can be saved from the parent site as either a file or directly to the Web Part gallery. After that the web part can be added to the sub site.
See http://sharepointontop.blogspot.com/2012/06/show-listview-webpart-from-parent-site.html for detailed instructions.
You can use content query webpart ,where you can display list from the parent-site and add the columns as per your requirement.
Are you getting the "List does not exist..." error when you try to save a SharePoint List as a web part in SharePoint Designer?
There is an easy but completely undocumented way to fix this. You must create a new custom view that uses a "Style" of "Basic Table". Then when you go into SharePoint Designer, click on that new custom view (I name all of mine SPDesigner just for simplicity / consistency), and then click inside the page and then click "LIST VIEW TOOLS >> WEB PART >> To Site Gallery". After you do this a pop-up window will come up asking if you want to maintain the original list data. If this pop-up does not appear, your web part will not work right.