Superman has three main characteristics; He is invulnerable, he is honourable and just, and he loves Lois Lane. Now how do you make a story out of that? What challenges can a man have who is incorruptible, and invulnerable?
There have been two main ways of doing this; Either you take away his immortality by using a magic rock; cryptonite, or you attack his girlfriend at the same time as you do the evil thing. Which has the nice side effect of having superman think about his morals a bit, but, this has all been done to death, and anyway, how do you change the morals of a perfect moral being? You can't. Any attempt at challenging his morals comes down to challenging his strength, because, as I said, he will always do his best. Superman is not corrupted, so he will sit in jail until he thinks he can no longer morally do so.
There is also this problem: If you want to use Lois Lane in this way, you are doing what is called "damseling". You are taking your only interesting female character and pressing her into the role of victim. If she could fend for herself, she wouldn't need rescuing, and so superman would not come. Which is a sad state of narrative logic to be trapped in as an independant woman. (PS: All women are, in principle, independent.)
Then what can we do? The answer is to break open each of these characteristics, to make them more flexible, and also to change some of the contexts within which his superheroing happens. Let us look at each of them in turn, starting with the last point.
The world of Superman is a very magic place. Superman flies in a magick kind of way, and the laser out of his eyes is also very magical. How about we put him into the real world of physics and biology? How about we put him in the world of hard science fiction?
This would put Superman under some interesting constraints. First off, he would no longer be able to fly at the speed of light. If you are approaching light speed, you are also approaching becoming light. The faster he flies, the more stress his body would take; so why don't we limit his speed of flight to something like 10% the speed of light, and make it really hard for him to get there; a true struggle. And let us also give him some acceleration, subject to the laws of inertia. Let us say he accelerated at 20mps(2). That would still give him superhuman speed, but he would be much more limited in how to navigate in tighter spaces, which would make the fighting sequences more interesting. He would also be subject to friction; so we could limit his speed in atmosphere to something like five times mach speed, which would explain why he goes to space to circumnavigate the earth; which would still only take him minutes by the way.
From a biological standpoint too, it would not make sense that his laser vision should be infinite. It takes a lot of energy to produce lazer, and his eyes could get tired. Making it a limited resource would mean that he would have to use it strategically in a fight. As it is now, he could easily have burned his way out of any situation if he so wished.
Superman is also much faster than us cognitively. He is able to catch a speeding bullet he himself shot. Mmm... With these kinds of powers, there is really nothing that would be able to hinder him in any way. He could sit in a chair for several milliseconds, thinking about a strategy that would take us a couple of hours, and then execute it with perfect dexterity. No, make him more like us. It'll make for a more interesting hero. Or, even if you want him to be much faster than us, let us highlight how that would be a problem for him. To him, we would all be very slow, and probably boring. It would help alienate him from our world, to make him feel like an outsider, which is an obvious theme for superman to explore.
What about Superman as an ethical being? Superman has very good intentions, and always does his best. How can one thwart that? Well, there are several ways. There are many ethical systems; some look at what kind of person makes a choice, some look at the intention behind the choices, and some look at the consequences of a choice to see if it was good. To make superman ethically interesting, we should let him meander a bit between these things. We should let him feel bad about doing something he intended to be a good thing, but had either bad consequences or sullied his character. Or we should have him do something he is uncomfortable with, because it is clearly the right thing to do. Or, we could have him live by steady principles, but discover that these principles have both good and bad consequences. Should superman save a person who is trying to kill themselves? Why not give him that choice?
A second thing to remember is that, there was a superman before superman, and that was Nietzsche's superman in "Thus spake Zarathustra". This person was not superior because of anything supernatural; but simply from having recognized that he or she must make their own choices in life of what is good an bad. Clark Kent, the superman, is after all an alien, and it would be interesting to see him fashion his own way ahead as to what is good and bad. That would be a comic worth reading!
Then about loving Louis Lane. I actually think this is one of the better things about Superman as a character. Many other superheroes do not have any real ties to this world, and if anything, the connection could be strengthened by having them have a child. That would give them both something outside of their relationship to consider, and it would also put a strain on their lifestyles. Should Louis Lane give up her job because superman can potentially do more good than she can through her journalism?
But the main problem is that there are not enough strong relationships. Superman should have some more human allies, some really good friends. She should have something else to do besides, something materially important to him. In other words, Superman should have a maximum of things he cares about and is willing to protect, because that makes him more interesting as a character, he also has more to lose, and at some point he may be forced to make a choice between many of the good things he cherish. Superman could end up having to confront himself, to say; This is who I am, where my allegiances lie. Maybe he'll say "Yes, I love my friend; but at this moment I can't be there for her because I have obligations at home, or maybe I need to save someone."
These are only some of the things we can do for Superman. By far the most important thing is to put effort into telling a good story. Those of us who have liked Superman for so long are really tired of seeing him save Lois Lane in spite of being shot with a kryptonite bullet. It is predictable and boring. Give superman some character, something to believe in, some flaws, some challenges, some restrictions; in other words, some life!