Given how they have been described in the books, I would say that any practitioner could *in theory* cast a death curse, however, *in practice* it likely doesn't make much sense to focus on anything but a wizard or above's death curse.
A death curse is a lasting magical effect that either has to be sustained by the sheer amount of power thrown at that last instant of death, or has to be tied to something else to keep the curse powered. Remember the curse has to last over the person day in and day out past all of these sun rises and the water that flows over them and whatnot. I imagine besides going ka-blewy, the only effective way to cast a death curse is to tie the spell to something else to keep it renewed. (Like Maragret's death curse was tied to her children.) Anyone who isn't a wizard likely doesn't have enough power or training to realistically create a death curse worth mentioning. They might have enough power to throw out a spell of vast proportions for them, but given what a wizard likely slings about, it's not something comparable or noticeable.
Also something to keep in mind is free will. I would argue that only a practitioner who has free will can cast a death curse. We get into a grey area with vampires as they seem to be creatures with far more free will than other monsters, but less than humans. Vampires aside though, most monsters shouldn't get a death curse. Faeries, old gods, dragons and the like are all bound by rules and limitation that might not be readily apparent, but forbid them from taking actions of true free will and thus cannot act outside of those restrictions. further, it is entirely possible that most of the power they wield are mantles of one form or another and the power of a mantle can't simply be used up and discarded, it must be passed to another individual (as logic would dictate by the very nature of a mantle of power).
Or maybe you die anyway if you use your death curse.
It is basically a spell that uses all your live energy cast by a wizard just before he is going to die using up all his live energy. If you do it to early and your enemy does not kill you you still die. That is why you should cast your death curse not too late but also not too early.
I'm pretty sure this is the case. The way death curses are described it seems like a last ditch effort to use up all the energy in your body you have left to cast one final spell in order to harm/protect/whatever at your target. While the wizard might have been effectively killed by whomever put them in the situation where they are using the death curse, it's always seemed like more of a final suicide option. The wizard, understanding they are doomed anyway, takes the reigns and says "I'm going out on my own terms".
Harry does almost kill himself with magic a few times in the book, just when he is slinging it around at his enemies. It's entirely possible if you don't stop yourself in time you could bleed yourself dry with magic, possibly with one big spell.
