If you had a fleet of carriers and battleships, plus three transports I immediately see one problem. You're bringing only 24 ground units with you. Number one, the best use for Marines is attacking from ships. Once you get that first coastal city it is difficult to move inland with marines. There should have been some tanks, artillery, and infantry as well.
Number two, you sounded like you had multiple carriers and battleships. I don't think that they were used properly if you could only get one city. From the context of your post I gather that your forces were pretty depleted after getting this city. Did you bombard and bomb this city enough before sending in the marines? I always pound the city into the ground before sending in ground troops. This way the enemy will be left with as close to one hit point as possible when I go in.
Back to my first point. You simply cannot, in this game, put all of your eggs into one basket and send only one troop type. You need artillery to wear down the enemy prior to a frontal assault. You need tanks to do most of the attacking. You need Infantry to hold the position after the tanks so that you're not wasting a tank in that role. You need bombers to break down that enemy unit that you didn't see before using all of your movement points. And you need marines to attack the coast.
I'm in a game now where the Indians were on a small island with about eight cities. The initial invasion brought me five of those cities before I had to grant peace because of the civil disorder in my country. I left what I thought were enough tanks and infantry to hold the cities, and moved my army to the northern continents where I just caught the Aztecs performing espionage. I didn't go to war with them, but I wanted to be ready.
Well, all of this time I was at war with the Russians who were allied with the Indians. When I made peace with the Indians I didn't make peace with the Russians - mostly because the only thing I ever saw from them was ironclads so they weren't a threat.
Well, I was bombing their ironclads whenever they went by India, and noticed that one of their cities was within bombing distance. I bombed it and the Indians declared war on me again. My country went into disorder - had to grant 50% luxeries - and almost immediatly lost one of their cities.
After reorganizing my troops in India I decided to just take them out. I moved my troops into position - almost all tanks - and lost almost my whole army in one turn using the tanks to attack the cities without support. Meanwhile, the russians landed and took that city I almost lost in the first turn.
Luckily for me I had some troop ships on their way to Aztecia which I turned back and landed - one with an army, and with a good mix of artillery, tanks, and infantry. I also rebased a lot of my bombers down there.
It took me about three turns to eliminate the indians from what was their island, and to regain my city the russians captured. I made peace with Russia and India (they had a few cities scattered throughout the world).
My point here is that I thought I could defend the country with a bunch of tanks, but was unsuccessful. Once I mixed it up a bit it was easy for me.