Is there a prefix that indicates that an event recurs four times a year?

Solution 1:

This is not exactly a prefix but the word does indeed refer to an event that occurs four times a year. And the word is "Quarterly".

Solution 2:

More importantly, is there a resource or table somewhere that I can use in the future to construct prefixes for other intervals shorter than a year?

Not really, because commonly used ones are often exceptions to rules. However, you now have a good set:

• Annually (and the multiplicators)
• Bianually
• Quarterly
• Monthly (there should be a word for every two months)
• Fortnightly
• Weekly

...

Now you only have problems if you need to define every 6 weeks or suchlike.

Solution 3:

If

quarterly

doesn't suffice,

tri-monthly

is probably closest in spirit to "semi-annually" (although I would prefer "biannual" to this anyway)

You should be able to construct such a table reasonably easily.

weekly           every week
bi-weekly        every two weeks
tri-weekly       every three weeks
monthly          every month
bi-monthly       every two months
tri-monthly      every three months
biannual         every six months

etc.