(Preface: Some people have taken offense at how pro-parent this answer is. There's good reason for this. In any meaningful interpersonal situation, we have to pay attention to the mindset of both parties in order to find the best solution. Everyone knows the mindset of the person who has to hear the child screaming. We've all been there. Those without children have not been in the position of the parent, so it's the parents mindset that is most valuable from the perspective of an IPS answer.)
Speaking as a parent, you don't have to tell us. We already know. In the end, there are only two major differences between your situation and ours:
- We're much closer to the source of the noise, so it's louder for us.
- We know it's our job to fix it. If we could, we would.
Going out to eat as a parent is a balance. On one hand, you don't want to disturb other clients. We know you don't want to hear our kid scream. Believe me, we don't want to hear them scream either. On the other hand, we want to be able to go out to eat as a family. We can't go to Chuck-e-Cheeses every day. It's a balance. We can't 100% capitulate to your desire for a quiet environment, and we can't 100% assume that we are the most important people in the world and do what we want, regardless of your ears.
Apaul34208 has the right idea. Talk with the restaurant management. They have a fiscal interest in keeping their clientele happy. They also employ people for their skill at resolving these sorts of issues. They can look at the eyes of the parents and figure out really quickly whether the parents need to be told to control their child, or if the best approach is to get you a seat further away from the commotion so that you and your wife can pay attention to each other.
If you do feel the need to take matters into your own hands, please watch our actions first. If we're trying to stop the screaming or if we're clearly stressed out by the screaming as well, there's really nothing you can tell us that would make the situation better. Only "alert" us to the issue if you're confident that we really didn't notice that our kid's screaming was a problem. I'm not sure how that could happen, but perhaps if the parents were drinking heavily and the kids were playing in a different room in the establishment...
And do fully expect us to respond with, "You're not a parent, you wouldn't understand." While it is rude and stereotyping, it's also rather true. It's really hard to understand what kids do to your life until you have them. Is it fair? Probably not. However, as a general rule of any interpersonal relationship, if someone is already close to their breaking point, pestering them will only make it worse, and the response should always expect in such a situation is a snippy response which firmly announces that they don't care about what you're thinking. Pushing someone who doesn't have the bandwidth to deal with being pushed always leads to conflict, parent or non parent.
If you watch the family long enough, you'll eventually see another parent couple leave the restaurant, walk past them and say, "We understand. We've been there," before walking away. Believe me, it's not fun to be in that position (or in the lavatory of a plane with a screaming infant on the way back from a canceled wedding. That's my horror story).
That being said, if you have any skill with kids yourself, and can go over and get them to stop screaming without issuing blunt force trauma or mental scarring, don't be afraid to get your hands dirty. Obviously, make sure the parents are okay with you interacting with their kid, but I'm not sure what sort of parent in their right mind would prefer a screaming kid over a happy one. If I can't figure out how to control my child, and someone else walks over and does it, I look at them with awe, not hate.
In the case where the parents don't care.
When interacting with parents that don't care, you quickly get trapped between the desire to help them learn and the desire to make them leave. I would still rely on talking to management. They still have a fiscal interest in keeping you happy. However, if I see that the family simply doesn't care, I use much stronger tone and words with management. As a parent, I want the benefit of the doubt, but I think I relinquish that benefit once I stop caring about others. I would expect some results from management. They may not be in a position to eject the family, but they should start treating you as a dissatisfied client. They might comp your drinks. Or they might only give you a "we're sorry," but they should do something. If enough people complain about the same family, they may act on it (such as in Curt's example in the comments, where enough people in a movie theater complained and caused management to eject the family). Certainly, don't suffer in silence. Let management try to make you happy.
If you do get in such a situation, focus on what they choose to do to try to keep their clients happy. They are in a bind between two paying customers themselves, and that's a delicate balance. The difference is that they're getting paid to maintain the balance -- you're the paying customer. Focusing on what people are doing to help you always improves the mood over focusing on those who are disturbing you. And then, afterwards, decide if you feel like patronizing that establishment again or not. It's your money. See if they earned it or not.
The Conflict Approach
In the comments, several people have had the attitude of "they just shouldn't be in my restaurant. They should be elsewhere." Now I can't dismiss this attitude, as much as I might like, but I can explain why you can't find an answer on Interpersonal Skills that goes down this route.
If you feel they just shouldn't have come to your restaurant with the kid (stay home, get a babysitter, go elsewhere, etc.) then we really have a collision of wants. They want something out of the night (they did go out to dinner). You want something out of the night (you did go out to dinner). If you believe they need to surrender their wants to support your wants, you are seeking a path of confrontation.
Are you in the right for wanting to seek confrontation? Maybe. That's a very complicated question. However, we don't need to answer that question to look at just the side effects of any confrontation, justified or not. In a confrontation, the results depend greatly on who is involved -- both you and the parents. If you are Liam Neeson, and you walk past my table, glare at my kid, and walk off mumbling something about a "special set of skills," I think I'll take my hint, ask for a check, and find somewhere else to be that night. If you don't look like Liam Neeson, I may not catch your reference. If I am a big bruiser, you probably don't want to tell me what to do. If I'm a shrimp and you're a big bruiser, maybe it's in your heart to push me around. Whatever happens, it's going to be hard to predict from afar. That's the nature of conflict. Always has been, always will be.
Given that the confrontational options are so specific to the individuals, there's no reasonable way you can get advice on a site like this on how to cope with your particular confrontation. The non-confrontational approach of going to management, who you are paying to put your wants before theirs, is reliable and can be recommended. You are welcome to come to your own conclusions involving conflict, but its just not feasible to help you come to that conclusion in this format.