The effect must be variable because I've read some people saying if you use a friendship day, brush your animal, take it to a dungeon, then take it to the town square that's supposed to give it a huge boost but I did that every day for a week and never gained another smiley face I don't know for how long you have to do it, but I stopped using my runeys on them because it wasn't going along that fast...in the long run probably faster, in the short run I don't care. Level 10 wool would be nice, but it's not worth the hassle.
I'm pretty sure all a friendship day does is start the day as if you have already fed and brushed your animals. So, if you have enough fodder for your animals, and you brush your animals that day, you've essentially done two days worth of work, in one day.
The reason why it may seem variable to some people, is that different animals have different amounts of FP needed to get to the next smiley face. Monsters found in the Green Ruins, for example, will gain smileys much faster than monsters found in the Towers. Also, the more smileys a monster has, the longer it will take to reach the next one. A monster will got from 2 smileys to 3 much faster than it will go from 8 smileys to 9.
Just because the results are not immediately evident, don't dismiss friendship days. They're doubling your FP gain, and that's never a bad thing.
It's easy to tell how your pet is progressing in FPs. A smiley comes every ten levels after it gains the first smiley one level after capture. For example, the Chitter in the Green Ruins is obtained at level 1. At level 2 it gets a smiley. Thereafter -- at levels 12, 22, 32, etc. -- it'll gain another FP.
Lower levels come faster. You can max FP gain on a Chitter (brush, take to a dungeon/Beach/Mountain Road for "X is happy" then to Town Square for "x is very happy"), one level per day up until about level 40. Then it slows to about one level every other day and so on.
Friendship day doesn't seem to make it go faster if you're maxing like that, but it should help if the monster is stuck in the barn because it's doing work. Or so it seems to me.