cited,”is” is the predicate and “entertainment is the subject which is singular in number.The rule is that the predicate follows the subject, which it governs, in number.

You could, however, also say:

Their main entertainments are puzzles and coloring.

All you have to look at is the subject, the noun that precedes the verb.

The verb has to be in accordance to the subject, not the object (puzzles and coloring)

How about re-wording it to make it sound right. Like:

‘Puzzles and colouring are their main entertainment’

or

‘Puzzles and colouring are their main forms of entertainment’

Because puzzles and coloring are two entertainments that means you are talking of more than one entertainment hence ‘are’ should be used.