How to be the most popular Lord in the Kingdom
You need to maintain your popularity above 50 if you don't want your peasants to start leaving your city. Since a couple of scripted events can have an immediate effect of -20 I would generally try to stay above 70.
You usually also want to be able to make as much money as possible while keeping your people happy. Below are some ideas on which can be the best way to combine these two goals, and thoughts on the cost effectiveness and other benefits or disadvantages of different methods of raising your popularity.
Ale Coverage gives you the highest benefit for the lowest cost. An Inn costs 25 gold and requires 50 wood. If you import the ale for 1 Inn for a year it will cost you 34.5 gold and give 30 peasants the maximum +4 popularity boost. You could then increase the taxes of those 30 peasants by 2 levels if you are taxing between Low and Mean; this would give you an extra 144 gold per year, meaning a profit of 109.5 gold per year. Of course if you grow your own hops and make your own ale you can make slightly more profit. Whenever possible then my people are kept well supplied with ale.
Increasing Rations is another good way of raising popularity if you can grow enough food. Looking at the cost benefits of using your excess food to increase your popularity, and therefore your taxes, compared to selling your excess food I came up with these figures. Note - food consumption is 0.2 units of food per peasant per month at the normal rate, 0.3 units at Extra Rations and 0.4 at Double Rations.
Ten units of food sell for 40 gold. 10 units of food will give extra rations to 100 people for a month which will give a +4 popularity rise. Increasing tax by 2 levels will usually give you a -4 popularity loss (-2 per level) and those 100 people will pay an extra 40 gold per month. In these cases there is then no difference between selling food or using it for extra taxes. In certain cases though there is a difference. Increasing taxes from Mean to Extortionate or Extortionate to Downright Cruel gives a -4 popularity drop in just that 1 level so in that case selling would be better. Increasing taxes one level from None to Low gives you a -3 popularity drop (from +1 to -2) but the tax increase is greater at this level and your tax increase from this for 100 people would be 60 gold and you would still be 1 popularity point in front. So in this case using the food for your own people is far better than selling it. In short I won't be selling food unless my tax rates are already at Mean or above.
The multiple food type bonus is nice to get but, while I might if possible try to grow a mix of food to get it, the figures show that importing food to achieve it is not at all cost effective.
Fear Factor Pleasant can increase your popularity but its disadvantages
are such that I would rarely use it. These are the initial cost of 30 gold per Good Thing and
the negative effect they have on productivity. This loss of productivity would often mean that
other better options such as extra rations for your peasants are unfeasible. For more
details see the Strategy article on Fear Factor
Religious coverage is another option for increasing popularity but, apart
from missions where it is a requirement, I would not normally use it. I haven't done any detailed tests as religious coverage depends a lot on the random walking of the priests which makes it hard to quantify, but my own feeling is that I doubt if it would be cost effective due to the high cost of building chapels, and the fact that once you do start to get coverage they demand the more expensive churches and then cathedrals or you get a negative popularity effect.
I guess my preferred method of keeping peasants happy while making myself rich can be summed up as - get them drunk, overfeed them, be mean with taxes, torture them a bit and let them stay heathens.