The best thing to do to increase friendship and to most likely get gifts back is to send gifts!
Here are a list of things you can send:
Special Gifts[]
These are all unlimited gifts Valentines Gifts
Collectibles[]
These gifts are items you own! So be careful what you give and who to!
Animals[]
All the animals in the game are available to give as a gift but some of them are not unlimited gifts and some are one's that you own!
To view the all the animals click here