An argument between lovers

Solution 1:

How about lover's squabble?

From Dictionary.com and Merriam-Webster:

squabble: a petty quarrel

squabble: a noisy altercation or quarrel usually over petty matters

NOTE on @k1eran's answer:

Interestingly, Dictionary.com and Merriam-Webster define tiff as follows:

tiff: a slight or petty quarrel

tiff: a small fight or argument about something that is not important

So, according to Dictionary.com and Merriam-Webster, squabble and tiff mean more or less the same thing.

Turning to Oxford Dictionaries, one finds the following:

squabble: a noisy quarrel about something trivial

tiff: a petty quarrel, especially one between friends or lovers

lovers' tiff: a trivial or short-lived dispute between lovers (as noted by @k1earan)

I wonder why the definition of tiff in Oxford Dictionaries references friends/lovers while the definitions in Dictionary.com and Merriam-Webster do not.

Solution 2:

lovers' tiff

(also lover's tiff) NOUN A trivial or short-lived dispute between lovers. — OD

EDIT I ran the ngram using options from other answer and comments and as deadrat commented lovers' quarrel is the most used, those of course they don't all mean exactly the same thing.

Also for simplicity, and on principle, I ignored ones with lover's not lovers'.