I have a Radio Shack 20/40 Watt Soldering Station. It was a gift from my friend Michelle when I fixed her TV many years ago. Thanks Michelle!
Normally I'd post a picture here, but I won't this time. I'm ashamed of my soldering iron. The tip looks like the mangled claw of some battle-wearied dragon. I've filed it down so much that only a nubbin remains. I've been meaning to buy one, but the stores don't carry it and their website doesn't list them anymore.
After some digging, I found that the Weller PL100 series tips will fit this iron.
(Image Credit: Weller Catalog, 2015, Page 65)
They even have the fine point one I want, a Weller PL138:
(Amazon Associate Link: http://amzn.to/1M897KB)
Even better, I found a pack of 4 assorted tips including the PL138 on eBay for $22, shipped!
I also read that the tips from an Eclipse Tools 900-035 soldering station will work too.
(I'm sorry if this seems like I'm shilling for Weller. I'm not. Not being able to find tips for this sucks, and I really hope that search engines will crawl this page so I can find it easily in a decade when I need to buy some more.)