Postscript: Romaji, color-coding & translation by mink.

It sounds like the vocals have been slightly tinkered with, pitch-wise, but the underlined names takes the higher/main melody.

Tintarella di luna means "moon tan" in Italian (like... "sun tan").

ティンタレラ・ディ・ルナ
お屋根のてっぺんで　小猫みたいにね
あの子と二人で　月を見ていたら
"ねェ　恋をしちゃった"

ティンタレラ・ディ・ルナ
お屋根のてっぺんで　夜明けになるまで
月を浴びてたら
二人の心は"ホラ　ミルク色よ"

ティン　ティン　ティンのお月様
ティン　ティン　ティンと
くちづけ　してくれたら　なんて素敵

ティンタレラ・ディ・ルナ
お屋根のてっぺんで　月夜の真夜中
ふたりで寝そべって　月を見ていたら
"ねェ　恋をしちゃった"

ティン　ティン　ティンのお月様
ティン　ティン　ティンと
くちづけ　してくれたら　なんて素敵！

ティンタレラ・ディ・ルナ
お屋根のてっぺんで　月夜の真夜中
ふたりで寝そべって　月を見ていたら
"ねェ　恋をしちゃった"

ティンタレラ・ディ・ルナ
お屋根のてっぺんで　月夜の真夜中
ふたりで寝そべって　月を見ていたら
"ねェ　恋をしちゃった"

お屋根のてっぺんで　"ねェ　恋をしちゃった"
月を見ていたら　"ねェ　恋をしちゃった"
しちゃった...　しちゃった

TINTARELLA DI LUNA
Oyane no teppen de koneko mitai ni ne
Ano ko to futari de tsuki wo mite itara
"NeE koi wo shichatta"

[Ts/Ka] TINTARELLA DI LUNA
[Ts/Ka] Oyane no teppen de yoake ni naru made
[Ts/Ka] Tsuki wo abitetara
[Ts/Ka] Futari no kokoro wa "HORA MIRUKUiro yo"

TIN TIN TIN no otsukisama
TIN TIN TIN to
Kuchizuke shite kuretara nante suteki

[Ts/Ka] TINTARELLA DI LUNA
[Ts/Ka] Oyane no teppen de tsukiyo no mayonaka
[Ts/Ka] Futari de nesobette tsuki wo mite itara
[Ts/Ka] "NeE koi wo shichatta"

TIN TIN TIN no otsukisama 
TIN TIN TIN to
Kuchizuke shite kuretara nante suteki

[Ts/Ka] TINTARELLA DI LUNA
[Ts/Ka] Oyane no teppen de tsukiyo no mayonaka
[Ts/Ka] Futari de nesobette tsuki wo mite itara
[Ts/Ka] "NeE koi wo shichatta"

[Ts/Ka] TINTARELLA DI LUNA
[Ts/Ka] Oyane no teppen de tsukiyo no mayonaka
[Ts/Ka] Futari de nesobette tsuki wo mite itara
[Ts/Ka] "NeE koi wo shichatta"

[Ts/Ka] Oyane no teppen de "NeE koi wo shichatta"
[Ts/Ka] Tsuki wo mite itara "NeE koi wo shichatta"
[Ts/Ka] Shichatta... [All] shichatta

Tintarella di luna
Up on the rooftop, like little kitty cats
Along with that kid, as we watched the moon
"Hey, we fell in love"

Tintarella di luna
Up on the rooftop, until dawn
When we soaked in the moon
Our hearts were... "Hey, they're milk-colored!"

Tin-tin-tin goes the moon
Tin-tin-tin it goes
As you kiss me, how wonderful

Tintarella di luna
Up on the rooftop, at midnight of this moonlit night
We lie, sprawled out, as we watched the moon
"Hey, we fell in love"

Tin-tin-tin goes the moon
Tin-tin-tin it goes
As you kiss me, how wonderful

Tintarella di luna
Up on the rooftop, at midnight of this moonlit night
We lie, sprawled out, as we watched the moon
"Hey, we fell in love"

Tintarella di luna
Up on the rooftop, at midnight of this moonlit night
We lie, sprawled out, as we watched the moon
"Hey, we fell in love"

Up on the rooftop, "Hey, we fell in love"
As we watched the moon, "Hey, we fell in love"
Fell in love... fell in love