IPA filter
The IPA Filter (a third-party, contributed module) displays X-SAMPA ASCII markup as Unicode IPA. The intent is to offer an easy and fast way to display the International Phonetic Alphabet in Moodle.
Fonts
In order to ensure that the IPA displays correctly -- especially the combining marks (diacritics) -- you will want to be sure to load at least one IPA-compatible web font. The Moodle IPA filter ships with two fonts that you can call, or you can use a carefully selected Google Web Font. In each case you will need to add a link to a particular style sheet in the HEAD area of Site administration > Appearance > Additional HTML.
Gentium
Gentium is the first font listed in the filter's 'font-family' so if you load it, it should display. Gentium is a slightly fanciful serif font that is very readable even at smaller sizes -- important when you are using unusual glyphs.
To use Gentium add something like this to your Additional HTML:
<link rel="stylesheet" href="URL_TO_YOUR_MOODLE/filter/ipa/gentium.css" type="text/css">
You will need to provide the root URL to your own Moodle site to replace "URL_TO_YOUR_MOODLE".