From the help for the published tag:
"This meta-data tag may only be applied to methods that reside in object of classes cWebBusinessProcess or cWebService, or objects of subclasses of cWebBusinessProcess or cWebService."
In 19.1 we added an extra class called the cWebComponent. The WebResourceManager which used to be a cWebBusinessProcess was also changed to a cWebComponent.
In other words, you can no longer use the published tag inside the WebResourceManager.
Judging from the code you have to add though, i think you can get away with making your own object based on a cWebBusinessProcess (actually obsolete since 19.1) or a cWebService and adding the method there (where the published tag will work )
Keep in mind that in the ASP you'll have to direct the call to your own object instead instead of the oWebResourceManager.
You might also want to check the help file for some more info on the cWebComponent, it will probably clarify a thing or 2.