Is there something as Google Sitemapper for other search engines too?

You can use sitemapper to create a sitemap.xml that you submit to Google.

You can use the Sitemapper for Google, Bing and Yandex which covers a good portion. I would suggest you google sitemap formats to see what you need for any others you want to list with. There are probably some other sitemappers out there, but then there are probably a bunch of search engines that take the .xml file as well as the three above so check and see what you need to know better of what type of program to look for.

I can not find CoffeeCup Google Site Mapper. Can anyone point me to it?

https://web.archive.org/web/20070205220309/http://mercedes.coffeecup.com/CoffeeSiteMapper.exe

This is from the post found here:

https://www.coffeecup.com/forums/sitemapper/here-is-coffeecup-sitemapper/

which states that at the time the software was free, so it may not have a limited trial period despite the links it has for purchasing it.

Or it won't work at all if it's based on flash.

If you have the HTML Editor, that has Site Spider. Not sure what Site Designer may have.

How can you find something that isn't there anymore? (presumably thats why it's labelled 'Discontinued')

Site Designer latest build has a site mapper built in, all you need to do is select the option for site designer to create a site map on export, and enter the domain address name. It then creates a site map with the domain and the pages, upon export.