Next year, Joe will be trying to find a job for himself otherwise he will continue delivering pizzas.
Does this verb tense make sense? Or am I supposed to use simple future?
I think "will try" is better here. "Will be trying" refers more to what will be happening at a specific point of time in the future, especially with another parallel action taking place, like in: "I will most probably be watching TV when you come home tonight", or a prolonged action in the near future: "We will be staying at home during the weekend". "Next year" is not really "near future", mostly because it denotes a relatively long span of time, and we do not know how long "trying to find a job" will take.
First of all, let me make it clear that I am neither an English teacher nor a professional linguist. I've never taken a single college linguistics class. However, the following is my opinion:
On a certain level of analysis (if I may use such an intellectual? phrase)
Easterner is right. Both Danish linguist Otto Jespersen (who developed Novial) and Charles Kay Ogden (1889 -1957) the developer of *Basic English (c. 1930) would certainly have preferred something more like Easterner's constructions. In fact, Ogden's Basic English goes even one step further and says that you don't even need the verb "try". Thus, your sentence in Ogden's Basic would be something like: "In the coming year, Joe will make an attempt at looking for work. If not he will keep on sending pizzas to persons."
In plain old vernacular American English, however, there is nothing wrong with saying "Joe will be trying". Any native speaker of English would readily understand it and I think that few of them would censure you for it.
* Basic English uses essentially just 875 words.
I wonder whether Ogden's Basic English was based on Orwell's Newspeak or whether it was the other way around. Did Ogden suggest all plurals be made by adding "s"?
Either "will try" or "will be trying" are okay. There's nothing wrong with the future continuous here: it fits the action just fine. There are, however, other things that need attention.
First: you don't the the coma after "next year". Second: your use of "otherwise" is incorrect. Let me rewrite the sentence.
"Next year Joe will be trying to find a job for himself. If he is unsuccessful, he will continue delivering pizzas."