Yes, if you are flying on paid tickets, have AA note in your reservation that you are honeymooners. Then, when you check-in, discreetly mention that you are honeymooners and ask the gate agent if they could do anything special. It is up to the discretion of the gate agent based on availability. A friend of mine got upgraded that way.

I'd also suggest this for the car rental, hotel, etc...Friends have gotten upgraded from compact to convertible and from garden room to a suite, that way!

Good luck!