To 'have the stomach for something'  means to have the kind of personality that gives you the determination or the ability to do things which are unpleasant or dangerous. If you 'don't have the stomach for something' it means you don't feel as if you have the skills or ability to do something. Usually, these expressions are used in relation to tasks that are unpleasant or morally questionable. You are more likely to hear this used in an informal context. Similar in meaning to 'having courage' or 'being yellow-bellied'.

1. This job requires someone who can make hard decisions, and I'm not sure David has the stomach for it.
2. I just don't have the stomach to do something so dishonest.
3. Luke had to leave the military because he realized that he simply didn't have the stomach for combat.
4. I didn't have the stomach to look her in the eye after what I had done.

1. As a business, we have never had the stomach to exploit our employees.
2. Would you mind doing these accounts? I just don't think I have the stomach for it today.
3. It appears the organisation encouraged some surprising initiation rituals that some fledgeling members didn't have the stomach to complete.

In informal contexts, the expression 'to have the stomach for' or 'to stomach' can refer to your tolerance for particular types of food, such as spicy, fatty etc.

1. I enjoyed the time I spent in India last year, but I realized that I don't have the stomach for spicy food.
2. I loved my trip to Italy, but after three months I don't think I have the stomach for another plate of pasta.
3. Since I changed my diet last year I just don't have the stomach to eat meat any more and I don't crave any sweet food either.