To solve this riddle, we must think outside the box and consider an unconventional solution. Here's one possible answer:

We can build a bridge across the river so that all three can cross safely without the need for a boat. This way, the tiger, the monkey, and the banana can all cross the river at the same time and without the risk of any of them eating each other.

Alternatively, we could use a larger boat that can accommodate all three animals and the banana at the same time. This way, we can transport them all across the river together without any risk of them harming each other.

The key to solving this riddle is to think creatively and to consider alternatives to the given constraints. By doing so, we can find a solution that allows us to transport all three animals and the banana across the river safely and without any harm.