This is sung to the tune of Yankee Doodle.

アルプス一万尺 - Japanese Children's Songs - Japan - Mama Lisa's World: Children's Songs and Rhymes from Around the World  - Intro Image

Notes

*"Yake-ru" means "to be jealous" - it's a pun.

*****

In the 1st verse of this song, it's actually a joke about dancing on Mt. Koyari because it's so steep and pointy that no one can dance on it. You need rock-climbing equipment to climb it.

Pronunciation:

アルプス(arupusu)いちまんじゃく(ichi-man-jaku)
こやりの( Koyari-no) うえで(u-e-de)
アルペン(arupen)おどりを(odori-wo) 
おどりましょう(odori-masho)

おはな(ohana) ばたけで(batakede)
ひるねを(hirune-wo)すれば(sureba)
ちょうちょが(chou-cho-ga)とんで(tonde)きて(kite)
キスを(kisu-wo) する(suru)

いちまんじゃくに(ichiman-jakuni)
テントを(tento-wo) はれば(hareba)
ほしの(hoshi-no) ランプに(ranpu-ni)
てが(te-ga)とどく(todoku)

おはな(ohana) ばたけで(batake-de)
ひるねを(hirune-wo)すれば(sureba)
かわいい(kawa-i-i)あのこの(anoko-no)
ゆめを(yume-wo)みる(miru)

やりや(Yari-ya) ほだかは(Hodaka-wa)
かくれて(kakurete) みえぬ(mienu)
みえぬ(mienu) あたりが(atari-ga)
やり(Yari) ほだか(Hodaka)

やりは(Yari-wa) ムコどの(muko-dono)
ほだかは(Hodaka-wa) ヨメご(yome-go)
なかで(naka-de)りんきの(rinki-no)
やけがたけ(Yakega-take)

いのち(inochi) ささげて(sasagete)
こいする(koi-suru)ものに(mono-ni)
なぜか(nazeka) つめたい(tsumetai)
いわの(iwa-no)はだ(hada)

いわな(iwana)つる(tsuru) こに(ko-ni)
やまじを(yamaji-wo) きけば(kikeba)
くもの(kumo-no) かなたを(Kanata-wo)
さおで(sao-de) さす(sasu)

ザイル(zairu) かついで(katsuide)
ほだかの(hodaka-no) やまへ(yama-e)
あすは(asu-wa) おとこの(otoko-no)
どきょ(う)(dokyo) だめし(dameshi)

なごり(nagori) つきない(tsuki-nai)
たいしょういけに(Taisho-ike-ni)
またも(matamo) みかえす(mikaesu )
ほだかだけ(hodaka-dake)

まめで(mame-de) あいましょ(ai-masho)
また(mata) らいねんも(rainen-mo)
やまで(yama-de) さくらの(sakura-no)
さく(saku) ころに(koro-ni)

アルプス一万尺 - Japanese Children's Songs - Japan - Mama Lisa's World: Children's Songs and Rhymes from Around the World  - Comment After Song Image

Comments

The 1st verse of this song and the chorus are used as a hand-clapping rhyme. There's a longer version of this song with 29 verses - the full lyrics in Japanese can be found here.

Naming of Japanese Alps:

William Gowland (1842-1922), an English mine engineer named the mountain range. It was introduced in a book by Walter Weston (1861-1940) who was an English missionary.

Check out Mama Lisa's Blog post about how Yankee Doodle Helped Start a Revolution in Japan to learn about the history of this song.

Listen
Watch
The rendition of this song in the video below includes the 1st, 2nd, 5th and 11th verses.
Please let us know if you think this video has been taken down by YouTube.
Thanks!

Thanks and Acknowledgements

Many thanks to Sadao Mazuka for the translation (with Mama Lisa), the commentary and the pronunciation.

1st Image of Mt. Yari and Hotaka: Wikipedia
2nd Image of Mt. Koyari from Wikipedia - edited by Sadao.

Arigato gozaimasu!