Consider suggesting some, please.
[name_u]Sunny[/name_u]
[name_f]Mere[/name_f] (pronounced like the [name_f]Mere[/name_f] in Meredith)
[name_u]Sunny[/name_u]
[name_f]Mimi[/name_f]
[name_f]Sue[/name_f] or [name_f]Su[/name_f]
[name_f]Zuzu[/name_f]
[name_f]Essie[/name_f]? [name_u]Or[/name_u] maybe an initial nickname like SJ.
[name_f]Merry[/name_f]
[name_f]Susi[/name_f]
Summer…
Sum
[name_u]Sunny[/name_u]
[name_f]Sunshine[/name_f]
[name_f]Sue[/name_f]
M&M
[name_f]Essie[/name_f]
Bummer (wonk wonk)
[name_u]Drummer[/name_u]
Hummer
[name_u]Cali[/name_u] (if they’re good at summing like a calculator 
)
I don’t think summer really needs an official NN. It is short, with 2 short syllables. A NN could possibly develop from circumstances in a child’s life.
I like [name_u]Sunny[/name_u] and Susu/Zuzu for [name_f]Summer[/name_f]. Also what about [name_u]Sam[/name_u], [name_u]Sammy[/name_u]? A wild card could be [name_f]Maisie[/name_f]?
Why does [name_f]Summer[/name_f] need a nickname?
[name_f]My[/name_f] favourites are Sam/Sum, [name_u]Sammy[/name_u] and [name_u]Sunny[/name_u].
Also
[name_f]Meri[/name_f]
Serry