Using two screws on a four screw ceiling mount

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The short answer is no.

Additional info: Your product should be installed per the guidelines the manufacturer intended. If they do not present a two screw mounting option you should not invent one. The engineering behind the scenes is typically done to ensure safety and not to mention, the brakets are intended to use 4 screws, using only two could deform the bracket and compromise the weight distribution from 4 points to 2 points, essentially doubling the force on two points.

Now... if the brakets are over engineered (which is pretty rare these days), and you've calculated the weight bearing tensile strength of your beam material and it is greater than the (max combined weight of the # of people on the hammock + the hammock weight) x 1.7 (to be safe),then no. You might be able to take your bracket to a big box store and find alternative brackets, but I would still easily double the max weight (or nearly double it), when shopping for the brackets they have to ensure it will still hold up and serve its purpose.