Trimonthly is, in fact, already in several dictionaries. Problem is, unlike its counterparts bimonthly and biweekly, trimonthly is only defined as occurring every three months, sans a secondary three-times-a-month meaning.
I would recommend thrice-monthly, if you needed to form a single word.
The committee meetings will occur thrice-monthly until this matter is
resolved.
EDITS:
As was pointed out in the comment below, the hyphen could be omitted as well.
Also, I'll restate my opening remarks, but add some links:
Although bimonthly can be used either way (see here), that doesn't appear to be the case for trimonthly (see here, here, here, and here). In light of such evidence, I'd be hesitant to use trimonthly when meaning "three times each month."
Often and oftentimes may be used with little or no distinction to mean again and again in more or less close succession, but oftentimes is occasionally preferred for intonational reasons ("He had a sense of humor which was sometimes loud, oftentimes lewd, but never deliberately unkind [...].")(1)
In the following NGRAM often is compared to oftentimes(2).
It would seem that the use of oftentimes is very rare in written English language.
(1) Merriam-Webster's Dictionary of Synonyms
(2) NGRAM is for written language only, of course.
Best Answer
Is there a -times word for rarely? Geoffery Chaucer certainly thought so when in The Clerk’s Tale he whilom wrote:
As you see, old Chaucer wasn’t much of a speller. 😼
We would today write his seelde time without spaces, spelling it sometimes seld-time or seldtime but othertimes written out more in full as seldom-time or seldomtime. And as ofttimes occurs with such adverbs for reasons too complex to explore in this question, we might also add an ‑s to make it seldtimes or seldomtimes instead.
Alas that seldtimes should be so seldom seen today, now that seldom is used for seldomtime’s purpose!
Historically, such adverbs have appeared under guise of all manner of spelling and punctuation. For example, in Measure for Measure Shakespeare wrote, albeit perhaps for the sake of the verse’s meter and rhyme, that
As with adverbs ending in ‑when, ‑while or ‑whiles, and ‑day or ‑days, people would form new adverbs by colliding shorter words with ‑time or ‑times anywhen they pleased. The OED attests such stunning adverbs as:
Although some of these adverbs were aforetimes written out as separate words, you should still think of them as single adverbs no matter whether they’re spelled with a space or hyphen or written with neither in keeping today’s preferred style of cleanliness. After all, in speech where they originate you cannot hear a space or a hyphen, so this is merely orthographic convention, not grammar.
Courageous writers might be unbewhile tempted to mint their own coinages of this sort as Chaucer and Shakespeare were themselves fearlessly wont to do. However, it is probably best that these adverb-making strategies not be thought of as productive combining forms nowadays unless you’re up for some feather ruffling.
In so unbending a world that even such unremarkable adverbs as daytimes or Tuesdays can freak out the unfamiliar, freely using agèd words like seldtimes risks making unfriends of an otherwise amicable audience.
Stick to seldom and no one will notice you — presuming, of course, that that is your goal. If not, then do as you please.