What language is "Spakoynee Nochay" in (I'm told it means good night),
and how would you say hello, good morning, and good afternoon in the
same language?  I believe it might be Russian or Kazakh and I might be
losing something in the translation from cryllic to western
characters.

Hello beckles and thank you for your question.

You were very close!

"Spakoynai nochi" is Russian for "Good night"

See:
"Spakoynai nochi" which simply means "Good night" in Russian"
http://www.russian-st-petersburg.com/2-news/2001-09.html

Also:

Zdravstvuite = Hello
http://www.everythingesl.net/lessons/world_helloday.php

"Dobroye utro" = Good Morning
http://www.elite.net/~runner/jennifers/gmorning.htm#R

"Dobry den" = Good afternoon
http://www.elite.net/~runner/jennifers/gaftern.htm

To hear how some greetings sound, have a look at the website below.
http://www.masterrussian.com/blday_greeting.shtml

Thank you for your question, and if you need any clarification of my
answer, do not hesitate to ask prior to rating my answer.

Very best regards

THX1138

Search strategy included:
"greetings in russian"
://www.google.com/search?hl=en&lr=&safe=off&as_qdr=all&q=%22greetings+in+russian%22&btnG=Search

Thanks for your quick response!

Not sure if it is lost in the links above or not, but although it
means "good night" it really translates to "quiet or peaceful night". 
In Russian you are often wishing someone something, like ...wishing
you a quiet or peaceful night...in this case.  It is the same as
wishing someone or congratulating someone with the New Year or with
any given Holiday.  Just a minor innuendo.
Peace.