There are three broad things in bhakti which can help us develop taste for any activity including chanting.
1 . Association (sangha)
Association with those who have taste. Just like if we want to develop taste in the study for shastra then we need to associate with those who have taste for shastra. Same applies to chanting. If we associate with those who are chanting seriously then we also get some taste for chanting.
2 . Intelligence (buddhi).
We develop our intelligence when we read the glories of the holy names. Using our intelligence, we internalize philosophically the importance of chanting.
3 . Desire (ichcha).
We try to cultivate the desire for chanting more and more.We should remember that the taste is something which is not in our control but our endeavor and desire to absorb is in our control.
What do mean by taste of chanting? Is it that we want to get taste in our chanting or we want to give Krishna pleasure during our chanting? Actually, the two are not unconnected. If we give pleasure to Krishna through our chanting Krishna will also reveals His sweetness and we will also get pleasure. We focus on trying to think of chanting as an activity of service to Krishna.
In the seventh chapter of Chaitanya Charitamrita, it is mentioned that Hari Das Thakur chanted the holy names for the pleasure of Krishna and thus he was able to chant so many rounds. Similarly, if we can strive to chant in the mood of service in which we strive to give taste to Krishna then by His mercy we will also get the taste.
Rather than focusing for taste of chanting we can try to cultivate absorption and focus in chanting and as a result of that taste will automatically come.