Defining Genocide
I show the genocide convention is nonsensical and botch an attempt to make a better one
From Wikipedia: any of the following acts committed with intent to destroy, in whole or in part, a national, ethnic, racial, or religious group, as such:
Killing members of the group.
Causing serious bodily or mental harm to members of the group.
Deliberately inflicting on the group conditions of life calculated to bring about its physical destruction in whole or in part.
Imposing measures intended to prevent births within the group.
Forcibly transferring children of the group to another group.
The individual sufficient conditions seem okay; the two problems are 1) the 'intent' to destroy and 2) the 'whole or in part.'
Let's start with 1) intent. A layperson may think that if you know that a consequence of your action is that X will result, and you do that action, then you intend to do X. But this is not the definition philosophy or law uses. Intent relies on a counterfactual: would you do this action even if X did not result from your action? In other words, if the action is wanted because it causes Y, it doesn't matter if X happens. You can think of X as the cost and Y as the reward. You may not wish to do Y if X is higher than Y, but it's still not the target.
The problem with this definition of intent is that it relies on narrative. You may say that the Holocaust is a genocide because Hitler intentionally killed Jews. But suppose you take the definition in this philosophical sense. In that case, one might appeal to something like 'Hitler intended to build a more harmonious society, he would have taken action towards this goal, even if there were no Jews, to begin with, they were just in his way!' and hence the Holocaust was not a genocide. With this definition, the set of genocides may become empty, so this notion of intent just boils down to who has the best lawyers to tell the more convincing story about the end goal.
The second part, 'whole or in part,' is just pure sophism. 'Part' can be anything; one member of an ethnicity is a 'part' of that ethnic group. The vagueness of the word has the effect of making more or less every targeting of an ethnicity a genocide; if one person targets an Armenian because of their ethnicity, that could potentially classify as genocide.
In sum, the 'intent' part has the effect of possibly excluding potential all genocides from the list, and the 'part or whole' has the effect of not excluding any killing at all! Which means it should not even be part of the convention.
Alternative
So, the legal definition is nonsense; it will all boil down to the narrative and judges' bias. However, people still use the word in everyday life; some definitions must exist to make sense of the words they use. What do most people mean when they say the word 'genocide'? I think you can make sense of most people's use of the term by simply using it as a subcategory of 'ethnic cleansing.' That is, if an essential means to achieve ethnic cleansing is 'killing,' then it is genocide. So, I would put it this way: 'Genocide is when you try to clear out, largely through killing, an ethnic group from a region or area.'
Okay, but who would you levy this charge on? If we say only states, then we exclude the Rwandan and Armenian genocides; hence, it does not capture what people mean. So, you probably have to extend its domain to include 'political groups'; even though that definition will become challenging to articulate correctly, it should be expansive. Alternatively, you can expand on how to include states. For example, you can say a state is responsible for genocide if it directly commits it on its own OR neighboring territory OR knowingly allows it to take place without taking significant measures against it.
The ethnic part is more controversial than it sounds. It means that you don't take into account the religion or ideology of the people you are killing. So, most things that Wikipedia categorizes as 'genocides' would not be genocides because it implies that if they had converted to the dominant ideology, their oppressor would have spared them. For example, suppose ISIS accepted membership from the groups they were killing, like the Yazidis or Iraqi Turkmen. In that case, the Bosnian genocide may not be classified as such because the Bosniaks were definitionally Muslim.
Similarly, the Cambodian genocide was mainly about ideology and hence excluded. I would say this 'ethnic' component is what causes the number of genocides to remain small or explode. If ethnicity is a necessary condition, then there would be a dozen or so genocides. If instead you can have an or statement like 'Religion, or Ethnicity or Geographic location or political affiliation', then you may have more than a thousand genocides throughout history.