What is the difference between being blessed and being happy? I really am torn sometimes when having the kids in my Religious Ed. class read scripture, on the one hand we've got the Catholic Good News Translation from St. Mary's Press (Breakthrough Bible) which they don't stumble over and has nice pictures and everything. 

And on the other hand we've got the old crusty falling apart St. Joseph's New American Bible which is not particularly archaic in language, but definitely less readable and absorbable for the short time I've got the kids.

The problem I have with the GNT is that it doesn't sound like Mass, so when I say "Blessed are the meek" and the bible says, "Happy are the meek" I've got to do some explaining.  Namely I need to explain how happy and blessed coalesce. 

The only problem is, I don't believe that happy and blessed do coalesce, at least not on earth. As Our Lady said to St. Bernadette at Lourdes, "I can't make you happy in this life, but I can in the next".  At that moment, she was blessed, she still died a painful and tragic death at a young age, but she was blessed - and maybe happy, but not happy as the world knows it.

So, why even use the word "Happy" to describe being "Blessed" isn't this a complete misnomer or do the transliterators expect everyone reading to understand this?

and furthermore, how does happy = blessed and how does blessed = happy?
The root senses of the words

As you have noticed, English has changed a lot since the first translations were made.  Now, the original meaning of 'blessed', according to the etymology, is 'consecrated', but it started to pick up a second meaning—over time it started to sound like more like the word 'bliss', and so, following on the idea of being consecrated, the idea of blissfulness or happiness was added to it. (This is explained at dictionary.com.  For another example of how unrelated words can influence each other's senses, compare how the word 'niggardly' came to be politically incorrect.)

It may also be instructive to look at the meaning of 'happy' in the past.  The word 'happy' comes from the word 'hap', meaning what happens by chance. The words 'mishap' and 'happen' itself are related; the former is a bad chance occurrence, and the latter is what just happens to occur.  The root meaning of 'happy' thus is what we might describe as 'lucky' or 'fortunate'—as the familiar saying goes, "happiness is based on happenstance". 

While we do not strongly associate the idea of good luck with 'happy' today, the association was stronger in the past, so the translators of the time may have preferred not to use it here, though people who wrote dictionaries would use it to specify when they said 'blessed' that they mean this sense.

Which sense is actually meant?

We can find out by looking at the original language.  While English uses 'bless' for both the idea of consecration and the idea of happiness, Greek has two different words: εὐλογέω (eulogeō) is to bless as in to consecrate, and μακάριος (macarios) is happy.

In the original Greek of the beatitudes, 'μακάριος' is used. So indeed the sense of happiness is intended here; Jesus is talking about the future happiness of people who are not traditionally considered to be happy, not the future consecration of people who are not traditionally considered to be consecrated.   

(In Latin likewise there are two different words -- benedico is to bless as in to consecrate, and beatus is happy.  It is from the latter that we get the name 'beatitudes'.)

But 'happy' is different from 'blessed' somehow

Now, as you say, you "don't believe that happy and blessed do coalesce, at least not on earth".  You have reason to say this, but this is less about the meaning of the words and more about their associations.  The idea of 'blessed' happiness is strongly tied to the religious idea whose name it shares and so we tend to use the word only in religious contexts or with religious feeling -- and because we make it a religious idea, we tend to think about it more and realize that real happiness is not of or in this world.

Because 'happy' has no such religious association, we tend to use it more lightly and don't think of it in such a way.  But the idea is still in the word; one may see it when we are talking about happiness in a philosophical but non-religious way, as when we speak of the saying of Solon, "call no man happy till he is dead"—the original Greek for the 'happy' here is also of the same root as μακάριος. 

So why change 'blessed' to 'happy' in the translation?

It's true that 'blessed' already has more of the connotations that one would want in this text.  But, especially for those not raised to religious terminology, the word is kind of obscure — and without use in a variety of contexts, it's hard for people to learn what a word means; the meaning tends to get muddled.  By updating 'blessed' to 'happy'—which we can do now that 'happy' no longer means 'lucky'—we at once make the original idea more accessible, and hopefully stimulate in the word 'happy' the kind of thinking about happiness we have already done when using the word 'blessed'.