Which is correct, or more correct?
B. I should have had a better answer.
I’m coming around to the idea that verbally “of” in that case is just a corrupted “have”. Though of course, over time, some folks never learn to use “have” and will write using “of”.
“Should have”
“Should of” makes no sense at all.
You are confusing ‘should of’ and ‘shoulda’.
“Should of” is simply an ignorant misunderstanding of the contraction, “should’ve,” and it’s wrong.
“Should have,” always. Or “should’ve,” but understand it’s a contraction.
Or the classic but less popular “shudda”.
As long as we are doing grammar. Had a disagreement with my wife about the following sentence. “The person acted in a cowardly manner.” I say the word cowardly is a adjective describing manner. She says its an adverb describing acted. She finished #2 in her high school class of over 600, so I’d like to win this one.
It’s an adverb modifying manner, and in turn the prepositional syntagm “in a cowardly manner” modifies “acted”.
My quick guess …
The wife is probably thinking in terms of “cowardly manner” being essentially meaningless without the “cowardly” – hence “The person acted in a manner” being a meaningless sentence, so the cowardly must refer back to the verb. But I disagree. “Cowardly manner” is a perfectly straightforward adjective-noun pair in an intransitive verb construction.
Consider the following parallel:
He slept a restless sleep.
It’s the same construction, but no one would doubt that the adjective “restless” modifies “sleep”, and no one would demand that it be the adverb form “restlessly” because it actually modifies the verb “slept”! Would anyone say “He slept a restlessly sleep”?
Yet in the same sense, “He slept a sleep” is sort of nonsensical, but it doesn’t change the above fact.
You were right. Your wife, despite her high schools honors, should of known better. 
You can’t have an adverb modifying a noun!
Adverbs do not modify nouns. It is an adjective modifying manner. It describes what type of manner the person acted in.
Let’s change the sentence slightly: * He acted in a brave manner.*
Would anyone suggest brave was modifying acted?
If *cowardly *were actually modifying acted, it would certainly be defying normal word order conventions. So if we put it in the more conventional order, would this sentence make sense?: He cowardly acted in a manner.
I think the confusion may be that the suffix “ly” is often used used to form adverbs, but not all the time. For example: That is a lovely rose or That was a sprightly dance. But in any case the part of speech in English is determined by the usage of a word and not an inherent property of a word. Look at how often nouns are verbed.
“Should of” is a misspelling of the contraction “should’ve.” Spell it the latter way, and it all works out: sounds the same and grammatically and orthographically correct.
ETA: Crap, missed Aspenglow’s reply. That’s all this is folks. It’s not “shoulda” or anything like that. People simply don’t realize that the word is “should’ve” and, since it sounds exactly like “should of,” or at least it does in most US English dialects, they spell it as “should of” without realizing the grammatical error in that rendering. There is nothing ungrammatical about “should’ve.” It’s a bit colloquial and perhaps a dialectal contraction, but it doesn’t break any English rules.
“Adverb with adjectival function” would have been the complete nomenclature, but you’re right, it’s an adjective.
“Should of” is the typical grammar error that is corrected in school in very early grades. The other posters have it right - “Should have” or “should’ve” (contraction).
“I Should have had” is the perfect tense of “to have” if I recall my grammar from the 1960’s.
“The person acted in a cowardly manner.”
Yes, Alley Dweller has it right. The general rule of thumb is that adverbs end in “ly”, hence the confusion. But… In grammar, in English, rules were made to be broken.
Acted - verb
“in a cowardly manner” - adverb phrase modifying the verb acted
“in” preposition
“a” article
“manner” - noun, object of the preposition “in”
“cowardly” - adjective modifying the noun “manner”
An adverb can modify an adjective…
“The extremely ugly dog bit my hand.”
The adverb “extremely” modifies “ugly” which itself modifies (describes) “dog”.
After all, it’s not an “extremely dog” it’s an “ugly dog”.
How ugly? “Extremely ugly”.
My vote is for cowardly as an adjective modifying manner and the prepositional phrase “in a cowardly manner” as an adverbial phrase modifying acted.
It’s a little more nuanced than that because the same word “cowardly” is clearly recognized as both an adverb and an adjective, and the question is, which one is it in this case? The poster describes the debate with his wife: “I say the word cowardly is a adjective describing manner. She says its an adverb describing acted.”
In this case it’s clear that “cowardly” is an adjective modifying the noun “manner”. It’s also true that “in a cowardly manner” is a prepositional phrase modifying the verb “active”. And we therefore conclude that Vicsage is right and his wife should of (or possibly shoulda) known better.
Edit: Curse you, dreamregent, for ninja’ing my post as I was writing it! I should of typed faster!
Thanks to all who answered my question. For some reason “should’ve” just skipped my mind completely. Yes, it does sound like “should of”.
Etymonline is a good website to learn about English words.
Adjectives often become adverbs when -ly is postfixed, but nouns sometimes become adjectives when -ly is postfixed. Coward is a noun, so cowardly is an adjective.
However, as the above link shows, cowardly is also an archaic adverb attested before the adjective! (And indeed, coward can be used as an adjective.)
TL;DR: Vicsage was right, not his wife.
Not all words ending in -ly are adverbs. The heart is a lonely hunter. Tomorrow will be a lovely day. “Cowardly” is just a plain old adjective meaning “with the characteristics or manner of a coward”. In fact, it is hard to use cowardly as an adverb. “He ran cowardly from the battle”.
-Ly can be used in two different ways to derive a form. Normally, adjective±ly makes an adverb, but noun±ly makes an adjective.
Here’s an article by a linguist discussing the “should of” error, and comparing its use in the US and the UK.
–Mark