There are three places to get a free berry daily in Sinnoh, with different berries in each location. Not only are they the juicy ingredient necessary for Poffin making, they're an absolutely essential component of competitive battling.
Floaroma Town - Pick a Peck of Colors Flower Shop
There's a girl in this shop that will give you a berry once per day. The berries she gives are common, but they're free, so we're not complaining
Route 208 - Berry Master's house (directly west of Hearthome City)
The man here, known as the Berry Master, will give you a berry once per day. The berries he gives are #1-30, randomly.
Pastoria Town - southwest house directly west of the PokeMart
The lady here will give you some pretty good berries. Ask her once per day and she'll give you one of the following berries randomly:
Above: Besides Floaroma Town, there are two other place in Sinnoh to get free berries
If there's a specific berry that you really need, you can always save before talking to each person, and if they don't give you the berry you want, you can reset and try again until you get it. Just keep in mind that not all berries can be obtained at each place.