The easiest\quickest way will be to create macros for the accents and tones, use the macros in the latex code, they will pass unchanged through the mapping process because the map files know nothing about tones. But note: the deva mapping file needs to be tweaked (I don't know how (yet)).
(A) To answer the question as asked, (1) change to a font that has double svarita, e.g. Shobhika Regular; (2) add the double svarita in directly: copy-pastethe ᳚ glyph from a character map, say; or insert the glyph directly via its codepoint number (^^^^1cda) like this, inside the transliteration scheme: nama!ste^^^^1cda.
(B) To answer the other question that will result:
The mapping file needs tweaking.
नम॑ः works OK outside the transliteration mapping environment
but not inside it:
The itrans-dvn mapping is folding overlapping-sets of classes of glyph strings into each other in a certain sequence, and presumably sealing them off from subsequent glyphs properly joining on. (It's regex-related. It'll take a while (for me!) to disentangle.) (Also, I notice my browser + this page does not shape them correctly either.)
For the transliterated text, itrans-iast mapping defines the input alias for svarita and anudatta, namely ! and -:
Define anudatta U+002D ; -
Define svarita U+0021 ; !
but does nothing with them. So: Make a copy of itrans-iast.map in a place where TeX can find it (say, your current folder). Call the file itrans-iast2.map and add these two lines after the first pass(Unicode) line in the file:
pass(Unicode)
svarita > U+0951
anudatta > U+0952
Then compile with Teckit_compile itrans-iast2 to produce the itrans-iast2.tec binary file. Then go into your latex code and change Mapping=itrans-iast to Mapping=itrans-iast2.
(Alternatively, you could also type them directly, as well: nama^^^^0951ste^^^^1cda astu^^^^0952 dhanva^^^^0951ne bA^^^^0952hubhyA^^^^0951mu^^^^0952ta te^^^^0952nama^^^^0951^^^^0903. Or use macros as shortcuts.
Define them as:
\newcommand\svarita{^^^^0951}
\newcommand\anudatta{^^^^0952}
\newcommand\doublesvarita{^^^^1cda}
and use them like this, being careful with spaces:
\Paragraph{nama\svarita ste\doublesvarita\ rudra ma\anudatta nyava\svarita\ u\anudatta tota\anudatta\ iSha\svarita ve\anudatta\ namaH. \\
nama\svarita ste\doublesvarita\ astu\anudatta\ dhanva\svarita ne bA\anudatta hubhyA\svarita mu\anudatta ta te\anudatta\ nama\svarita H}
MWE
\documentclass[12pt,varwidth,border=6pt]{standalone}
\usepackage{fontspec}
\newcommand\mysktfont{Shobhika Regular}
\newfontface\fplain{\mysktfont}% no mapping
\newcommand\devtext{
\fontspec[Script=Devanagari,Mapping=itrans-dvn2]{\mysktfont}}%mapping transliteration to Devanagari
\newcommand\iast{
\fontspec[Mapping=itrans-iast2]{\mysktfont}} %mapping transliteration to IAST transliteration scheme
\newcommand{\Paragraph}[1]{\devtext{#1}
\par\medskip
{\iast{#1}}}
\begin{document}
\fplain
नम॑ः
\Paragraph{
nama!ste^^^^1cda rudra ma-nyava! u-tota- iSha!ve- namaH. \\
nama!ste^^^^1cda astu- dhanva!ne bA-hubhyA!mu-ta te- nama!H
}
\end{document}
Question Extending .map file with U+1CDA Vedic tone double svarita relates.
