Carlo's a tough call. He's pretty much a goofus. I would think that the Corleones would want to make sure that Connie lived comfortably,and raised a nice family.
So here's some speculation:

1) Set him up in a (legitimate) trucking or waste management business. Even as a front man,he could show income,pay taxes,etc.

2) This next one is a bit off the wall,but how about a Casino Host in one of Sonny's properties? Before you laugh too hard,consider this:

Casino Hosts are the guys that recruit and cater to the "Whales" meaning the top high roller gamblers.
Carlo has the wheel and deal personality,and could certainly develop connections to score high demand sold out tickets to sports or entertainment events.
Other perks include luxury suites with a Butler and Personal Chef,private chopper flights to the Grand Canyon for romantic picnics with their female friends,
24 hr use of a Limo and Chauffeur, 5 figure "gifts" for Mr & Mrs Whale,etc,etc. The list goes on.

This job would keep him under the watchful eye of Sonny,provide a comfortable living for him and Connie,and generate a nice additional income in the way of tips.
Hosts are legitimate hustlers in the Gaming Industry,and I think Carlo could do OK.

What do you all think?