A word for killing a cousin
Almost every type of killing can be described in a single word such as suicide, parricide, genocide, etc.
Is there such a term for killing a cousin specifically?
To my knowledge, there is no such accepted term. As Josh points out, parricide can be used to refer to any close relationship, though the main sense is that of killing a parent (i.e., patricide and/or matricide).
For lack of an accepted, specific term, you could use one of two fairly rare, but etymologically sound, neologisms that have been coined:
(con)sobrinicide
Killing your maternal cousinpatruelicide
Killing your paternal cousin
These are derived from Latin (con)sobrīnus ‘mother’s sister’s child’ and patruelis ‘father’s brother’s child’. To anyone with decent Latin skills, they should be self-explanatory and obvious, though they probably won’t be to others; and no dictionary that I could find has included the words (yet).
I think parricide is the correct term to use in your case:
The murdering of one's father, mother, or other near relative.
One who commits such a murder.
Source: Killing one's relations:
Source:http://en.m.wikipedia.org/wiki/List_of_types_of_killing
@Josh61 gives a good answer using existing terms, but it shouldn't be too difficult to coin a more specific term - or is it?
All these killing words are hybrid constructions, combining the -cide suffix (which can be traced back to Latin cida "cutter, killer, slayer") with a first element that is usually derived from Latin or Greek. So all you need to do is find a good Latin or Greek work for cousin and append the suffix, right? You can even use a non-Greek or Latin base, since the existing terms already mix up Latin and Greek (sui is Latin, geno is Greek) and give language purists the hives.
The only problem is that in most classical languages, there wasn't a single, encompassing word for cousins. Latin has several terms like cognatus, which can be used for more general kinsmen. Or maybe sobrinus for maternal cousins, or patruelis on the father's side. Other languages also have many different words for specific relationships:
Many IE languages (including Irish, Sanskrit, Slavic, and some of the Germanic tongues) have or had separate words for some or all of the eight possible "cousin" relationships, such as Latin, which along with consobrinus had consobrina "mother's sister's daughter," patruelis "father's brother's son," matruelis "mother's brother's son," amitinus "father's sister's son," etc. Old English distinguished fæderan sunu "father's brother's son," modrigan sunu "mother's sister's son," etc.
So choosing the exact term to base your -cide on might be difficult. If you have a very specific killing-word in mind, you could use a specific Latin term. Or, perhaps, just stick to Josh61's more general parricide.