How to cite a reference whose cite key contains '&' in the table

Since you have provided no example I haven't tested this (but confirmed to work in comments above).

You can hide the & if you used

\newcommand\zzzz{{\cite{2007A&A...465..587S}}}

in the preamble, and then used \zzzz in the table

If the cite works in normal text it would work in standard latex tables, so the problem must be with the deluxtable macros you are using (but just not using & in cite keys, and sticking to simple [:a-zA-Z0-9] would be good advice)

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Example added by CarLaTeX

EDIT: This is the MWE I used to test it (maybe does it works also with deluxtable macros?):

\documentclass[10pt,preprint]{aastex}
\usepackage[english]{babel}
\usepackage{chemformula}
\usepackage{natbib}

\newcommand{\kH}{{\cal H}}
\newcommand\zzzz{{\cite{2007A&A...465..587S}}} 

\begin{document}

\begin{deluxetable}{lll}
\tablecaption{blablabla. \label{tab:bla}}
\tablehead{
\colhead{Species} & \colhead{Model atom} & \colhead{A + \ion{H}{1}}
}
\startdata
\ion{Li}{1} & \zzzz & BB3\\
\ion{C}{1} & \citet{2015MNRAS.453.1619A} & \kH $^1$ = 0.3 \\
\enddata
\tablecomments{blablabla}
\end{deluxetable}

\bibliographystyle{plainnat}
\bibliography{bbb.bib}

\end{document}

And this is the bbb.bib file:

@book{2007A&A...465..587S,
  author = {Author, A. and Perche Alsuno},
  year = {2007},
  title = {A duvenen propri vusa kel simbul la},
  publisher = {Publisher},
}

@book{2015MNRAS.453.1619A,
  author = {Alexeeva, A. and Mashonkina, P.},
  year = {2015},
  title = {Keschi l e nurmal},
  publisher = {Publisher},
}

I don't know how much this is similar to the original, I invented the \kH command and I don't know if the OP uses natbib or what else and with which style, however the result is this:

According to BibDesk you should not use & in a citation key:

... characters " "@',#}{~%" (including the space character) are never allowed, while you will be warned if you use one of "&$^" in a cite key. Cite keys are essentially TeX commands, so you should avoid using underscores, for instance, if you ever need to print the actual cite key itself.

EDIT: According to comments below, the quoted info is not 100% correct. I'll post a better if I find one.