Can you post pictures of the little critters ?

Without seeing, you could try Volck Oil or if need be, Sevin.

http://www.discoverneem.com/neem-oil-insecticide.html

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Neem oil does work, but the way it works is different from other insecticides. Neem is not an instant, knock down, kill everything pesticide.

Neem enters the system and blocks the real hormones from working properly. Insects "forget" to eat, to mate, or they stop laying eggs. Some forget that they can fly. If eggs are produced they don't hatch, or the larvae don't molt.

Obviously insects that are too confused to eat or breed will not survive. The population eventually plummets, and they disappear. The cycle is broken.
"

if you want instant results, you'll need chemicals.

since your pests are munching at night, spray chemicals at night, then rinse off in the morning to reduce collateral dmg to the beneficial insects.

Mostly what I see are the Cuban May Beetle or the scarab beetle they call a June bug or June Beetle. The link below has some pictures of the little pains in the a$$e$. They will devour your foliage in unbelieveable fashion. They will eat almost anything if push comes to shove, but they love mamey sapote and mamoncillo over eveything else. I haven't seen them on my carambola as of yet, but they will eat young lychee leaves and they also love abiu blooms. I was shown a little trick that can help control them. You set up a bright flood light or other lighting fixture on a ladder or stool. Place a bucket of soapy water just in front of and below the light source. They re attracted to the light. When they crash into the light fixture, they fall into the soapy water and die. I have tried various oils. I didn't see very much result. Sevin will take them down. I try not to use anything stronger than that and I don't like using it unless I have to. Good luck.

Here is a link that might be useful: Beetles

Sounds like Cuban may beetle, but I haven't heard of them attacking the carambola. The best way to get rid of them is to kill the grubs (they start off as grubs that live on grass roots). There are two ways to do this - use a grub pesticide (bayer makes one, can't remember the name) or get rid of the grass. Once you get rid of the grass, it takes about a year for their populations to decline substantially. After getting rid of my grass, I still get a few from the neighbors' yards, but it's about 10% of what I used to get. They don't seem to venture very far.

Jeff

Yup. They are Cuban may beetles. They tend to bite the leaves of my mamey. I got a bug zapper and it reduced the amount of beetles biting my mameys by about 70 percent. There still some bite marks, but at least they are not completely or mostly bitten-up like the older leaves my mamey had, before I got the bug zapper.

A Bug zapper, of course! I'm going to buy a 1000 acre model that looks like the Eiffel tower tomorrow.

Jeez, do they still make bug zappers? I haven't seen one in 30 years or so.

I do not have grass any more. I removed it last fall and put 5" of mulch down, but my neighbors all have grass. Grrr...

I got mine from Lowes. There are many levels of bug zappers from smallest to largest when it comes to acreage coverage. I'm pretty sure Home Depot has them also.