Generate exciton with parallel/anti-parallel spin How can I experimentally generate excitons, controlling the spin-polarization of the participated electron and hole to be either exclusively parallel or anti-parallel?
 A: I fear your question is not very precise. Unfortunately my reputation is not high enough to allow me to comment instead of answer.
What exactly do you mean by the term "exciton"? The way it is normaly understood, is a pair of one electron and one hole. So there are no multiple electrons whose spins could line up parallel oder antiparallel.
In a biexciton (two holes, two electrons) or a trion (either one hole, two electrons or two holes, one electron), you can have two electrons. Then of course you can have triexcitons,... with any number of electrons.
You can create excitons for example optically in a nanostructure (typically quantum dots (QD), nanowires oder quantum wells (QW)). 
Two possibilities to control the involved spins are optical pumping of a doped QD (see Atatüre et al.) or selective tunneling (see e.g. Kroutvar et al.)
But you have to keep in mind, that any situation with two electrons aligned parallel (or in the more general case of many electrons: more spins aligned in one direction) will be quite shortlived. 
EDIT: Taking into account the holes, actually keeps most of my answer valid, as it only adds information where I generally talked about controlling the electron spin. Producing excitons in quantum dots via circularly polarized light (spin +-1) will result in the spins of electron (spin +-1/2) and (heavy-)hole (spin -+ 3/2) antiparallel for reasons of angular momentum conservation. Using for example the optical pumping technique from M. Atatüre, using a third state for transition into a dark state, can enable the access to a state with the electron spin aligned to the hole spin. Alternatively you could aim for a selective tunnelling scheme, producing several excitons and allowing only certain carriers to leave the diode structure (see the Kroutvar paper). This becomes significantly easier, if trions are ok for you.
But again, it is crucial, which lifetimes you are aiming for, what you want to allow (trions?). Optical excitons are generally  limited to lifetimes in the order of 1ns. 
