Ceremonies are important- every human culture has them. They mark our passage through life, from birth, through adulthood, marriage, parenthood and death. Without them, your post-apocalyptic society may not collapse, but it will lack cohesion- it will be less of a society, and more of a loose collection of individuals. It’s time to think ceremony.
Now, there won;t be the time and resources to perform the ridiculous, over-ornate and costly ceremonies that exist in the west, but ceremonies will still need to exist. ANd as a leader, you will probably have to lead them, in order to solemnise them and make them seem legitimate in the eyes of your followers. Cermonies have another advantage, one the church exploited in medieval europe- if someone misbehaves, you can restrict their access to these necessary markers, effectively making them a non-person. Cunning, hey?
Birth ceremonies are important- they mark the new child as a member of society, whether it’s the simple registering of their name or a complex and ornate christening. These are often naming ceremonies as well. In many cultures, naming something makes it ‘real’. In fact, many cultures used to believe that children who died without being baptised would return as vampires. Most naming/birth ceremonies involve the child being officially welcomed to the world with a gesture of some kind- sprinkling water on the head for example. Water will probably be at a premium, so you can’t do that, but how about smearing dirt on the child? Make up some nice-sounding stuff about how this marks the child as a part of this place, entitled to the protection of the group, blah blah blah. There you go. Happy parents, a sense of belonging and good-will existing throughout the tribe.
The western world has replaced tribal initiation cermonies with alcohol and vomiting, but that doesn’t mean it’s not important. Marking someones ascent into adulthood means a number of things- it means they’re a full and contributing member of the group, with all the rights and duties that entails. The rite can be complex, or it can be simple. I’d reccommend a test of skill of some kind- ask them to fetch a useful *something* from beyond your boundaries, or to reach a certain point a decent and challenging distance away. It should be something that doesn’t involve dreadful risk, but isn’t so easy they could do it with their eyes shut. A rite of passage like this makes your young people feel proud and useful, and encourages them to work hard.
People will fall in love, and want to spend the rest of their lives together. A lot of them will want some kind of mark of their decision, a way of publicly making the promise. Who are you to deny them? Marriage ceremonies can be complex, or they can be simple, but at their heart all they involve is two people making a promise. It’s up to you how complex you make this, but remember it should be celebratory and joyful.
Funerals are more for the relatives than the deceased. With limited space and fertile land, cremation will probably be necessary, rather than burial, but there’s no reason you can’t have a standard ceremony to allow closure for the community. Ensure it follows the logic of your other ceremonies, allow friends and family to speak about their dead loved one. Perhaps even enforce a few minutes of silence afterwards.
With ceremonies you can control your population, and ensure their happiness and mental helth. You will build a society. After a few generations, the ceremonies you adopt will be second nature- they will be tradition.