Is there a word like "conjugate" that means switching a noun between plural and singular forms?
Changing a verb to reflect the number of people and tense of the sentence is called conjugation.
Is there a word that means toggling a noun between singular and plural?
ie. "The computer program could construct basic sentences, but it could not pluralify nouns correctly".
Verbs are conjugated. Nouns are declined, and different ways of doing that are called declensions.
decline (In the grammar of Latin, Greek, and certain other languages) state the forms of (a noun, pronoun, or adjective) corresponding to case, number, and gender.
[ODO]
However, changing the word to account for number (for example, adding an -s) is a form of inflection. Adjectives in English are not inflected for number: the same form is used no matter how many things are being described.
inflect Grammar Change the form of (a word) to express a particular grammatical function or attribute, typically tense, mood, person, number, and gender
[ODO]
Having had regard to @Andrew Leach, in his answer, and the comments it provoked, I think the all important word is number.
However number would be a difficult term to use without there being ambiguity. Saying that the program could not specify number would introduce the idea that you needed quantity specified in some way.
Can't you just get by with could not specify nouns as singular or plural?
I am not as knowledged as others here about our English language, but I did stumble across this: http://www.thefreedictionary.com/singularisation
I suppose one verb would be "singularise". It feels right to use, although I must admit I can't recall it ever being used and additionally I find the spelling to be odd.
Based of speech, I would personally spell it & sound-it-out like 'singulise' (sing-gul-lise).
Regardless though, The word sounds right to me and I would think most native english speaking people would understand the context without much problem, but either way the spelling does still looks strange to me.
the only other thing I was wondering, is whether you could simply say "depluralise" which would effectively imply the same thing.
This is a really VERY intriguing question you have raised! :)