Contraction for 'are' with nouns

Solution 1:

Is this correct?

the candys 're in the box

It's not usually considered correct but it is sometimes encountered.

the womens're at the car

That's wrong for other reasons.

I know 'you're', 'we're', 'they're' are valid usages, but can it be used for nouns?

No, not usually.

Solution 2:

Here are the top 21 ’re forms in the Corpus of Contemporary American English:

               TOT      SPOKEN   FICTION   MAGAZINE  NEWSPAPER  ACADEMIC
1   YOU'RE     244694   108878   65509     44733     22486      3088
2   WE'RE      195472   117655   26890     19939     28368      2620
3   THEY'RE    169989   94821    22991     23922     25776      2479
4   WHAT'RE    777      12       721       24        17         3
5   THERE'RE   442      169      211       23        33         6
6   HOW'RE     393      135      234       13        9          2
7   WHO'RE     189      18       130       29        11         1
8   WHERE'RE   142      2        129       5         4          2
9   WHY'RE     66       4        60        2                    
10  YE'RE      56                51        4                    1
11  THAT'RE    33       7        20        3         3          
12  'RE        24                22                  2          
13  YOUR'RE    19       3        7         6         1          2
14  HERE'RE    18       3        9         4         1          1
15  IFYOU'RE   15                          14                   1
16  PEOPLE'RE  15                14        1                    
17  HELL'RE    14                14                             
18  GUYS'RE    11                10        1                    
19  OWE'RE     10                1                   9          
20  THINGS'RE  10                10                             
21  THOSE'RE   10                10                             

As you can see, forms other than you’re, we’re, and they’re are quite rare in comparison. For the most part, they occur primarily in fiction, although there’re and how’re occur with some frequency in spoken English.

Of course, the two examples given in the original question are not correct because the plural of candy is candies not candys and the plural of woman is women not womens. There were no examples of candies’re in COCA, but there was one example of women’re.

Solution 3:

No, it's not correct. You'd have to say:

the candies are in the box, the women are at the car

Solution 4:

We would write The candies are in the box. If a native English speaker says that sentence out loud, they may pronounce it so it sounds more like The candies're in the box. (But we would never write it that way.)

Another example:

We would write The cars are in the parking lot.

If a native English speaker says it out loud, it might end up sounding like The cars're in the box (but we would never write it that way).