Hello, I ran into a problem, I wish to marry Shahvee, the only Argonian available for marriage. Problem is It won't allow me to marry her. I have a house and the Amulet of Mara. My only dialog options are "Why are you so happy?"
Please Help.

Have you tried asking he why she's so happy? It could lead to a quest. As far as I know so far, marriage candidates will open up once you've done quest(s) for them. You mind me asking where she's located? I might want to check it out personally.

I had the same problem. Hunted for an answer for ages before giving up and marrying my argonian to a non-argonian.

PS Despite not being able to marry her, there are male argonians walking around right next to her that gave me the option for marriage....

Found out where she is. I'll go check it out.

Windhelm's docks. She has a quest to retrieve a stolen amulet.

Shahvee is the only Argonian Female for marriage, and has a quest that must be done before she will marry. She's in Windhelm at the Argonian Assemblage.

There are two male Argonians available. Derkeethus in Darkwater Crossing, needs to be rescued first, and Scouts-Many-Marshes, also in the Argonian Assemblage, Windhelm. Scouts has a quest, as well as being a light armor trainer.

Pity that there are no Altmer males....

What are the conditions for her quest. I have talked to her many times at various levels.

The only condition I can think of that I have not met is that I haven't joined the Stormcloaks.

I'm also having the same problem as the OP with regards to Shahvee not giving me the amulet quest on my latest character. Oddly, Branwulf isn't giving me his quest to stop bandits either. I've done both of these quests before so their sudden inaccessibility is befuddling.

Why would you want to marry an Argonian? They must smell horrible after six.

Silly lizards. Slaves can't get married!

I didn't join Stormcloaks or Legion and still got her quest, so you can rule that out

Get out :/

Never,

I've asked why she is so happy and she still only has that option. I can only ask her about her happiness or not talk at all. lol

You have to do a general-favor-type quest for her first. The reason I call it that is because there are about a dozen of these general "favor" quests for NPCs like that and only one of each type of Radiant Story thread can be active at the same time because they have the same governing quest ID.

Finish up other radiant story/misc quests you have (like grab X from Y dungeon for me, or deliver this thingy to that guyamagig in whatsis place) then go back to her. She'll now most likely offer you a quest - complete that and she'll like you.