There is no simple rule, I'm afraid. Let's look at the General British English canonical pronunciation of some
'lunch box, 'lawn mower, 'book-case, 'lawn party, 'garden party, a'larm bell, 'smoke alarm, 'shoebox, 'coat hanger, 'mountain bike, 'Oxford Street, etc. There are a lot of noun compounds with primary stress on the first constituent. This looks promising, but alas ...
... despite 'Oxford Street it's Oxford 'Road, Oxford 'Circus, Oxford 'Court, Oxford 'Drive, Oxford 'Gardens, Oxford 'Lane, Oxford 'Avenue, x 'Mews, x 'Close, x 'Square, x 'Station, etc., and we can add other place names such as Epping 'Forest, Wandsworth 'Plain, Ladram 'Bay, Cumbria 'Fells, Derbyshire 'Dales, Maze 'Hill, Leckwith 'Moors, Buckingham 'Palace, Albert 'Hall, Westminster 'Abbey, Stone'henge, Hyde 'Park, St. Paul's Ca'thedral. Widening our geographical perspective we note Niagara 'Falls, North 'Sea, Atacama 'Desert, Eagle 'Plains, Yukon 'Territory, etc.
Needless to say noun-noun combinations are not restricted to geographical names. And it's here where it's getting really complicated!
olive 'oil or 'olive oil but 'olive branch yet olive 'drab,
peanut 'butter, butter 'icing but 'butter bean,
'milk tooth but milk 'shake, milk 'chocolate, milk 'pudding,
'coach station, 'coach driver,
neighbourhood 'watch, but 'watchmaker, 'watchcase, 'watchdog,
'soap dispenser, 'soap opera, 'soapbox,
back'bencher but 'backbreaker, 'backbone,
crown 'colony, crown 'court, crown 'jewels,
pound 'note, pound 'sterling, but 'pound cake,
apple 'pie, apple 'green, apple 'sauce but 'applecart, 'apple blossom, 'apple tree,
head 'start, head 'waiter, head'quarter (or 'headquarter) but 'headroom, 'headset, 'headlight, 'headline.
On the 24th of December 2010 I wrote (the text is completely looney):
Before Christmas 'holidays start I do my Christmas 'shopping: I get some 'Christmas cards and buy some 'Christmas presents: On Christmas 'Eve I put them into Christmas 'stockings, so my beloved ones will find them on Christmas 'Day before we all have Christmas 'dinner, which includes some Christmas 'pudding. We might watch or listen to the Queen’s Christmas 'speech and sing some Christmas 'carols round the 'Christmas tree. Later we eat 'Christmas cake or might pull Christmas 'crackers. I no longer give out 'Christmas boxes. On the whole 'Christmas time means a lot of stress.
Have I whetted your appetite?
P.S.: See also Jack Windsor Lewis's remarks on stress irregularities.