The fixed presentational phrase Here/There is/are ...,
- Here is the coffee ~ There is the cream ~ Here are the saucers ~ There are the spoons.
as well as the existential phrase There is/are ...,
- There is a unicorn in the garden ~ There are some people here to see you.
are prone to contraction, like all fixed phrases.
- Here's the coffee ~ There's the cream. /hɪrz/ and /ðɛrz/
But contraction with are is difficult with here and there, because they already end with /hɪrzr/ and,
so adding another /ðɛrzər/ syllable afterwards makes it hard to hear the difference.
Here's the coffee ~ There's the cream. But contraction with are is difficult with here and there, because they already end with /r/, so making them disyllabic by adding another /ər/ syllable afterwards makes it hard to hear the difference.
Here're the saucers ~ There're the spoons. /'hɪr(ə)r/ and /'ðɛr(ə)r/
Here're the saucers ~ There're the spoons. /'hɪr(ə)r/ and /'ðɛr(ə)r/
Consequently they are uncommon as contractions in the language. However, it's extremely common to use the singular monosyllabic contraction (Here's, There's) even before a plural noun phrase.
This is because the subject does not precede the auxiliary, but rather the reverse. English number agreement works only forward, except for archaic and vertiginously pedantic constructions like Here am I or There is he.
Consequently the way these would be said in normal conversation is
- Here's the saucers ~ There's the spoons. /hɪrz/ and /ðɛrz/
As for whether to write these, that depends on your relation with your Inner Grammar Teacher.