Transliteration of Egyptian uses all these four characters as well, and several fonts have been made specifically for Egyptian transliteration based on classic typefaces. Unfortunately, though such fonts exist based on Garamond (Aegyptus/Nilus) and Bembo (Cardo, for general philological use), I’m not aware of any which are based on Caslon.
Adobe Caslon doesn’t have the dot-below diacritic at all (neither combining nor spacing), so even Billy’s suggestion of combining two glyphs won’t work without some extra tweaking.
There is, however, a free (OFL) Unicode font called Junicode, which is based on an early-17th-century font which is quite similar to Caslon. While there are some fairly obvious differences between Adobe Caslon and Junicode if you compare them directly – in particular, Caslon’s italics are much more slanted than Junicode’s – they’re not a half-bad match visually, particularly if it’s only these specific characters.
This is what Adobe Caslon Italic looks like with a GREP style in place to apply Junicode Italic and 8° skew to ḥ, ḍ, ṣ and ṭ:
Not an exact match (the ascender on the d is higher than other ascenders, and the slanting still isn’t quite a match), but I would venture that if this is for a technical periodical and these characters only appear occasionally and not all over the place, very, very few readers will ever notice.
If you don’t think this blends in well enough, I think you’ll have to split the precomposed characters up into sequences of the base letter and the combining dot below (U+0323), and then use a separate font (such as Junicode) just for the dot-below and adjust the kerning between the letter and the diacritic, as Lauren’s answer and Alan’s answer suggest in the thread Billy linked to.
There’s a good chance you’ll have to create separate character styles for each of the four letters, but you can still use them as GREP styles quite easily.