Toning?

Depends on how you "naturally" tone the coin.

If you place a coin in an album or a slab it's still going to tone, but at a MUCH slower rate.
If you place a coin on a windowsill in sunlight it's going to tone much faster.

Both are considered natural.

I live in south Texas and am starting to experiment with natural toning. I'm rigging up a felt lined box that I'm going to inset into the top of my dash. (Don't freak out it's a company truck and I'll make it look nice.) I've going to set it up to where I can have about 16 or so different coins toning at any given time. I'm interested to see what the affects of 100 degrees (probably closer to 150 in the cab) and some seriously intense sunlight will do to different coins and the speed at which it will do it.

Chlorine is also an element of coin toning. Trace amounts of chlorine are left behind in paper from the bleaching process. It's effects are very fast acting in large amounts. I tried Chlorox on a junk coin to see what would happen and I had a black coin in a matter of minutes. I was able to watch it go from bright silver to rainbow to black, it was an interesting experiment, but very uncontrollable.

is it possible to have uneven toning?

For natural toning a coin can tone unevenly, on one side only, horribly, not at all, etc. There are many substances that create toning in a coin. And as well there are many reasons it can be stopped or deminished. Since toning is in reality a chemical reaction of metal with other substances, it will and does vary massively.
For example if a coin is left in the area of a pool that has been treated with Chlorine, a coin laying on the ground in an area where a steel mill once was in operation, near a power plant that burns sulfur rich coal it may or may not tone. Some coins are handled by people in gas stations and become oily so they would not necessarily tone due to a protective covering. However, some coins would tone from that same oil pending the material of the coin.
There are many people that play around with toning of coins. Some of the better results are from heating a coin. Of course the method of heat, the amount of heat, the burning material all make for different results.
One of the things I like to do is buy cleaned coins since they are usually much cheaper. Then place them on a window sill in the kitchen. If a lot of cooking is done in that room, the amount and variety of gasses present normally will tone down a cleaned coin to make it look almost normal. Some have come out so normal it is almost impossible to tell they were ever cleaned. The problem is what is cooking though.