I'm sorry but I don't think there's anything that the government can or should do. Morality is dwindling more and more everyday but fixing it isn't something that's the job of the government. Morality is something that has to be passed down from parent to child, it's got nothing to do with the government whatsoever.
I also believe that as far as moral standards are concerned, this present generation is almost completely a lost cause, to fix things, we have to start from the next generation and train them up the right way.
Notwithstanding this fact I believe that if the government where to do anything at all it would be along the lines of the following.
1. Create a course called moral education for high school and primary school kids. I believe that this would go a long way in letting kids know what is wrong from right, that way even if they aren't getting the proper orientation at home, they'll get it in school.
2. Lead by example: I don't know if this holds in other countries but in Nigeria, members of the government are the chief propagators of immorality. The constant looting and corruption in government officials should stop, children follow what you do more than what you say so if they see people doing the right thing, they'll do the same.
3. Create judicially punishable moral laws: Certain acts like indecent dressing, sexual immorality and so on should have laws drafted by the legislature which prohibit or at least regulate how these things can occur.
I hope this helps
I too conclude, that today's world is a morally twisted and messed up place. The wrong values are praised (greed, lust and selfishness) while the good ones are laughed upon and even considered to be weaknesses (kindness, generosity and respect).
Your question is a tough nut to crack because the governments themselves are the ones pushing their citizens into the botomless pit of immoral behaviour. They allow, propagate and even fund the messages that promote these kind of actions in people. It's a well known worldwide trend that has been going on for at least ten years now.
Just take a look at what kind of crap is shown on TV nowadays, especially in some parts of the world.
So, without relying on the government, read enemy, people should thrust themselves to try to not to be influenced by the outside world trying to transform them into the worst version of themselves.
I don't believe moral standards to be going down in the world. On the contrary, to me it seems that the world is becoming a more peaceful and just place decade by decade. But if it were true, I don't think government is the answer if general moral standards were to be dwindling because in that case, governments would be subject to the same moral decay as societies in general.