My suggestion is that at the first mention of the word atom, you add a qualifier like neutral and/or ionized. For example, you can use one of the following constructions:
...neutral or ionized atoms...
...both neutral and ionized atoms...
...atoms, whether neutral or ionized, ...
...atoms, both neutral and ionized, ...
After that, just use the word atom. The reader will know that you mean both neutral and ionized species.
In parts of the text where it is important to distinguish electrically neutral species from electrically charged ones, use the expressions neutral atoms and ionized atoms.
In many (though not all) contexts, the word atom already denotes both the ionized and the non-ionized species. This is why when it is important to emphasize the status with respect to electric neutrality, we speak of neutral atoms and ionized atoms.
I agree that the default reading of the word atom is one where it is electrically neutral. But I disagree that electric neutrality is part of the very definition of that word.
(As others have emphasized already, an ion is not necessarily an ionized atom; an ionized molecule is also an ion.)
Wikipedia is of course not itself a reputable source, but consider the second sentence in its article on atoms (boldfaced emphasis mine):
Every solid, liquid, gas, and plasma is composed of neutral or ionized atoms.
Here are some examples of similar usage from published sources (boldfaced emhases mine):
A rare-earth or actinide atom, whether neutral or ionized, very often possesses several electrons outside closed shells... (source)
identified by the spectra of their neutral or ionized atoms (source)
Tables of Spectral Lines of Neutral and Ionized Atoms (source)
the fact that both neutral and ionized atoms are emitting (source)
In all of the examples, it is clear that the authors say that atoms can be both neutral and ionized, which wouldn't make much sense if atoms were neutral by definition; see below for more on that.
To be sure, there seem to be examples where electric neutrality seems to be part of the definition of the word atom. For example, in the university-level introductory-chemistry textbook by Zumdahl, we find the following:
Since atoms were known to be electrically neutral... (p. 46)
But Zumdahl is not consistent in this usage. Consider his definition of an ion:
An ion is an atom or group of atoms that has a net positive or negative charge. (Zumdahl, p. 56)
This definition would make no sense if atoms had to be electrically neutral by definition; if they did, it would not be possible for an atom to have a net positive or negative charge. To drive this point home, note how strange the above definition becomes if atom is qualified by neutral:
?An ion is a neutral atom or group of atoms that has a net positive or negative charge.
'How can a neutral atom have a net charge??' is what we immediately want to ask. In order for the sentence to make sense, we would want to rephrase, e.g. as follows:
An ion is a neutral atom or group of atoms that has acquired a net positive or negative charge.
Now it's OK, because a thing can change group membership after something happens to it; compare with an odd number is an even number to which we added 1.
Similarly, if it were really the case that atoms were electrically neutral by definition, it would be a bit strange to talk about neutral atoms—after all, what other kind could there be? And yet, we find the following in Zumdahl (boldfaced emphases mine):
In a neutral atom of each element, how many electrons are present? (p. 71)
...the symbol and mass number of a neutral atom whose total mass of its electrons is... (p. 74)
Note that the first electron is removed from a neutral atom (Al), ... (p. 309)
The number of valence electrons on the free neutral atom... (p. 364)
Zumdahl is definitely not alone in using the expression neutral atom. It is in fact widely used in scientific literature, as a search in google books can easily verify (see here).