This is indeed a truly difficult task. When counting carbs for your diet it helps (a little) to know that your body can't process dietary fibre. That means you can subtract the grams of fibre from the total grams of carbohydrates. You can't do that for any other item on the nutrition label. That number is the true net carb for the food.
- Spinach has 4g fiber/100g -- 1g net carb
- Green beans has 3g fiber/100g -- 4g net carb
- Sugar snap peas have 3g fiber/100g -- 4g net carb
- Sweet Peppers (green/yellow/orange/red) have 3g fiber/100g - 4g net carb
NOTE: your lettuce/cabbage has very low calories and generally runs 1g fibre/100g product -- 1g net carbs. It's a good filler.
You are going to get your best results in the dark green vegetables. The good news is you also get a number of vitamins and minerals your body needs from these vegetables. Unfortunately, you won't find anything with an incredible 9g fibre that doesn't have a commensurate amount of other carbs. Something you may do while you are cutting carbs is to use Fibre supplements. I've been able to find some that give me 4g fibre/serving with a net 2g carbs. That can help a lot.