This word appears twice in 1985 by Anthony Burgess:
‘That’s it. Without us how would the Christniques get on?’
They go out wanting to be cracked. Then they practise the Christnique of loving your enemies.
According to Wiktionary, "nique" means "A small thing" in French. I know that sometimes the word "nique" is used as a vulgar word.
From the context, I believe that Burgess is using "Christnique" in two different ways.
In the first phrase:
Without us how would the Christniques get on?
"-nique" seems to be used as a Latinised form of the common suffix "-nik", which the dictionary tells us is:
a suffix of nouns that refer, usually derogatorily, to persons who support or are concerned or associated with a particular political cause or group, cultural attitude, or the like
which is used to form words such as beatnik and peacenik. So Burgess is coining the term "Christnik" as a slightly derogatory term for Christians.
In the second use, however:
Then they practise the Christnique of loving your enemies.
"Christnique" seems to be used here as a portmanteau between "Christian" and "technique", to refer to the Christian doctrine of loving your enemies, as a tool to convert non-Christians by good example.
It is a while since I read Burgess' book; it may be a spelling variant of the suffix -nik, used by Burgess' characters in the novel to refer to those who profess Christianity as their religion or practise it.
