Possible but not so straight forward.
first, see https://www.scirra.com/tutorials/624/te ... box/page-1
I don't know whether you can truly do all the HTML charade like in regular website on the textbox of C2 alone. If it's possible, that would simplify your problem quite greatly.
Nevertheless, with respect to the tutorial above, what I would do is creating a Sprite Font that has two colors in it.
For example, you have the default black letters and red letters. And refer to the red letters in the "character set"  by using unicode characters such as â’¶â’·â’¸â’¹â’ºâ’»â’¼â’½  .
Also, continuing from the tutorial above in this case, in the event sheet, you would want to check for the text input and see if the input has any matches with certain strings that you want. You will then replace all the characters in such string with their alphanumeric counterparts. Now, you will have certain red words or phrases in your text. It's quite hectic and lots of works.
Perhaps somebody could suggest a more elegant way?
 - from Sprite Font, C2 manual:
A string of characters that describes the sequence of letters in the sprite font image. This is used to map text to images. While the default starts with the English alphabet, it could be changed to another language or sequence and the image updated accordingly. Note however the Sprite Font can only display characters that are in the character set; any characters not in the character set with a corresponding image will appear as an empty space.
[quote:ry7dsweu]Enclosed Alphanumeric from https://en.m.wikipedia.org/wiki/Enclosed_Alphanumerics