"FIFO" (First In First Out) refers to the memory queuing mechanism - not the memory matrix itself. Therefore, it's possible to implement a FIFO using either RAM or Registers (Flip Flops) as the memory matrix.
With that said - registers are considered an "expensive" resource (compared to RAM). Therefore, if you don't need the functionality of a register - it'll probably be wiser to implement your FIFO's memory with RAM.
In your case, if all you need to do is store a single 60 bits wide vector - I don't see why you'd need a FIFO.