How would PageManager know what content to use to create "target"?
Why not just check if target exists & create it yourself if not, with whichever template you want to use?
Page page = "pagePath";
ResourceResolver resourceResolver = getResourceResolver();
Resource parent = resourceResolver.resolve(pagePath + "/target");
PageManager pageManager = resourceResolver.adaptTo(PageManager.class);
if (parent.getResourceType().equals(Resource.RESOURCE_TYPE_NON_EXISTING) {
pageManager.create(pagePath, "target", "SOME_TEMPLATE_NAME", "SOME_TITLE");
}
pageManager.copy(pagePath, pagePath + "/target/newPage", null, true, false);