Finding the proper ASCII character for superscript "r"?

There are no superscript letters in ASCII. ASCII contains only the basic Latin (English) letters A–Z, a–z, digits, and a small collection of other characters. There are only 128 code positions in ASCII.

In Unicode, there are more characters (about 1,000,000 code positions, about which a little over 100,000 have currently been assigned). They include “ᵉ” U+1D49 MODIFIER LETTER SMALL E, which belongs to the Phonetic Extensions block, which means that it has been included due to its use in phonetic notations, not due to use in normal writing systems of human languages. I think it is the “superscript e” that you have found; I cannot imagine what else it might be. There is really no law against using such characters as simple superscript letters, but it isn’t particularly recommendable either.

Anyway, there is no corresponding “r”, simply because a superscript r is not used in phonetic notations (widely enough).

In general, superscript letters as often used e.g. in English “1st” or French “1er” should be regarded as stylistic variants of normal letters rather than independent characters. At least this is the Unicode position, which is what software vendors normally adhere to. So you cannot indicate superscripts at the text level but at a higher “protocol level”.

Depending on software context, this could mean 1) using superscript command in a word processor like MS Word (select letter(s) and use a formatting command); 2) using sup markup in HTML; 3) using Opentype sups feature, when supported by the software and the font. The last option is the only typographically really acceptable: it means using a superscript glyph designed by a typographer, whereas the other options use just reduced-size letters and place them higher