Well, I think lethal injection would be the most suitable for the modern age. In the western world firing squad still is seen more militaristic by it's nature - like Warlord is using it for martial law.
But when I made the graphics I did some research as usual.
I found out that in countries which still practice execution shooting has usually replaced or became optional for some previous methods like hanging (although both are still used, like strangling, stoning and beheading). It also has been increasingly common method in civil executions since WWI, before it was used mainly by the military. And even they started to use it in late 18th century, not immediately after. In US it's often been optional, a state to use it usually has also another more popular method.
Electric chair was an industrial era innovation, in the spirit of enlightment it was seen to offer less public and more humane method than hanging or shooting. But only country which uses it today is the US, and it was rarely (if at all) seen anywhere else.
In the same spirit of enlightment many countries in the world ceased to execute people in peace time. In for example Finland there has not been peacetime executions after 1918, after the civil war was settled.
Same with gas chamber, which replaced electric chair. I don't think it was used anywhere else than the US (well, of course in Nazi Germany). Lethal injection replaced gas chamber in it's turn and is the most popular method in the US today. At the moment injection is used in 38 states, electrocution in 8, gas in 4, hanging in 3 and firing squad in 3. I remember reading somewhere that firing squad would be the top choice if convicts could always choose for themselves.
Lethal injection is without doubt the most modern, serene and least painful way for a country to get rid off its unwanted. In addition to the US only China, Guatemala, Philippines and Taiwan use it.
But when you look at the rest of the world guess what method is the winner? Firing squad!
It's used in 73 countries, and is sole method in 45 countries. Silver goes to hanging, 58 countries and sole method in 33. Bronze medalist is (at least for me) a bit of a surprise: the ancient way of stoning, which is used with other methods in 6 countries. As said, injection in 5 countries takes the fourth place and fifth comes from the dark ages - beheading. Divided sixth place goes to earlier mentioned electrocution and gas chamber with one country to use them. Strangling is still used in some places and again somewhat startling news is that in Sudan people are sometimes crucified.
When planning I always have to think about is cool graphics to fit into civ building concept. I used the platform which was under the gallows as a base for all methods to give these executions a public nature and to remind of this cruel heritage from primitive ages. Even though people are civilized enough not to watch executions publicly they still often approve it in silence.
Graphicswise firing squad is far more exciting to look at and draw than a concrete chamber with a heavy door or a bed and a doctor, who is giving an injection to tied patient. So I made it this way, which according to what I've learned is far more realistic than to have an electric chair in modern era. Still, as said injection was my first thought because of it's modern status.
Anyway I don't think humane methods exists, since execution is only humane to everybody else than the victim.