I think a good way is to use the puzzles. Select the more valuable ZZ items, then put one valuable egg at end. Paying all puzzles every day usually you can get one puzzle where you can go to end and get the egg.
Keep doing all the parts of the game. Feed pets. Send the airship. A lot of people don't know that you get coins for the items you pack into the crates. Do daily quests. Catch morphing flowers. Play dice and Trina's slot machine. Spin the wheel of fortune. Open the treasure chest in your private room and it one of your friend's rooms. Do the puzzles. The absolute best way, though, is to do rounds of HOS. It's the most reliable, and, unlike the dice game, you don't lose money.
Coins are pretty easy to get. You just have to have patience and let the quests rest while you accumulate the resources you need to complete them.