Since you’re using fontspec, instead of loading tipa, you should select a Unicode font that supports IPA. If you can use fontspec, you no longer need the legacy package tipa. If you have a lot of data transcribed in \textipa format, consider using a script to auto-convert it. You can enter your IPA symbols as UTF-8, using the input method of your choice, or a character map. In fact, you can do this in LaTeX 3 even if you use the tipa fonts.
You could simply pick a main font that has IPA symbols, but here is an example of switching to a supplementary font.
\documentclass{article}
% Changed the geometry to fit in a TeX.SX MWE
\usepackage[paperwidth=10cm, paperheight=4cm]{geometry}
\usepackage{fontspec}
\defaultfontfeatures{Scale = MatchLowercase}
\setmainfont{EB Garamond}[Scale=1.0]
\newfontfamily\ipafont{Charis SIL}
\usepackage{polyglossia}
\setdefaultlanguage{english}
\disablehyphenation
\DeclareTextFontCommand\textphonetic{\ipafont}
\begin{document}
In the bigynnyng god made of nouȝt\footnote{Nouȝt: nought \textphonetic{/nᴐ:t/}}
heuene and erthe.
\end{document}
Here, I matched Garamond to Charis SIL (which is actually based on Bitstream Charter). Other free fonts that contain IPA symbols include Doulos SIL (matching Times), Andika, Gentium Plus and DejaVu Sans. The Unicode clone of Computer Modern that does is CMU Serif. Many commercial fonts now do as well.
An alternative to defining a \textphonetic is to use ucharclasses to automatically load a different font family for IPA symbols. This package has been abandoned for years, however, and only works in XeTeX. If you’re really turning hyphenation off, I would strongly recommend you compile in LuaLaTeX and \usepackage{microtype} to get font expansion. This will improve your word spacing immensely.
I don’t recommend it, but: should you want to keep using tipa commands, you can look up their Unicode values and patch them in individually.
\newcommand\textopeno{{\ipafont\symbol{"1D10}}}
or more simply, to use the currently-selected font
\newcommand\textopeno{ᴐ}
Technically, it is possible (in theory) to keep using the legacy tipa encoding in the same document as Unicode using luainputenc, but if I said anything more about that, poor Ulrike Fischer might have a heart attack. And she doesn’t deserve that.
PS
Frank Mittlebach correctly adds to my answer that the reason you’re getting this error is that tipa does not appear to be properly installed. The T3 Computer Modern Roman font that your TeX engine is looking for as a fallback ought to be installed on TeX Live 2019, but isn’t being found.
Even so, I highly recommend using Unicode over the legacy 8-bit encoding. The advantages include the ability to enter IPA symbols in your source file, and to copy, paste and search your PDF.
Based on a comment from him, the following workaround answers your literal question, which was how to use the 8-bit cmr font from tipa with fontspec. I don’t recommend it.
\documentclass{article}
% Changed the geometry to fit in a TeX.SX MWE
\usepackage[paperwidth=10cm, paperheight=4cm]{geometry}
\usepackage{tipa}
\usepackage{fontspec}
\defaultfontfeatures{Scale = MatchLowercase}
\setmainfont{EB Garamond}[Scale=1.0, NFSSFamily = cmr]
\begin{document}
In the bigynnyng god made of nouȝt\footnote{Nouȝt: nought \textipa{/n\textopeno :t/}}
heuene and erthe.
\end{document}
As of July 2019, the font families this works with on CTAN are cmr, cmss, cmtt, phv and ptm, but more are in the pipeline now that it’s possible to make T3 fonts from OpenType fonts automatically. You could produce a T3 font from an OpenType font locally—but there is literally no reason whatsoever to go through that rigmarole if you have the Unicode font and are already using fontspec. (The only conceivable reason to ever do this is to work around the requirements of a site that only accepts 8-bit encodings but allows you to supply your own 8-bit fonts. Someday soon, I hope, those sites will catch up to this century.) You would need more work to enable UTF-8 IPA symbols in your input this way as well.
