Searching MyFonts for "circled numbers" gets you stuff like Fyra. But if you don't anticipate your lists being that long, there are more choices.
① to ⑳ and ❶ to ⓴ are in encoded in Unicode. Here's all the fonts on MyFonts that contain the character ⑨. Some of them don't go up to ⑩ but you can see there is a lot to choose from.

Find Fonts, Advanced Search, available characters, contains, ...and paste in a character the font needs to have (from whatever source is most handy, like the character map application, unicode.org charts, Wikipedia... I'm working on a font family that has them, so I copied it out of the Metrics window in Fontlab).

One way would be to click through to each specific font's page and select the tab that says Glyphs, which shows you the whole character set. But to make it much easier to compare them all, just copy from this: ①②③④⑤⑥⑦⑧⑨⑩⑪⑫⑬⑭⑮⑯⑰⑱⑲⑳ and paste it into the sample text field at the top of the list, the place where it probably says "[Pangrams]".