One could argue that Friar Laurence, Lord Capulet, and the Nurse are the main characters who are most responsible for Romeo and Juliet's tragic deaths. Friar Laurence is the person responsible for marrying the two lovers in secret, coming up with a plan for Juliet to fake her own death by drinking his sleeping potion, and informing Romeo that his wife is not dead inside of her family's tomb. Unfortunately, Friar Laurence's letter informing Romeo of Juliet's situation does not reach him in time and Romeo truly believes that Juliet is dead, which is why he commits suicide.

The Nurse is also responsible for their deaths because she acted as the intermediary for the two lovers and helped Friar Laurence orchestrate their marriage. Without the Nurse's involvement, the two lovers would more than likely not be able to get married. Since their secret marriage is the cause of their heartbreak once Romeo is banished, one could also blame the Nurse for their deaths.

The third character responsible for Romeo and Juliet's deaths is Lord Capulet. Since Lord Capulet insists that Juliet marry Paris and is not aware of her secret marriage to Romeo, Juliet is forced to seek Friar Laurence's help and ends up receiving the sleeping potion. One could argue that if it were not for Lord Capulet insisting that his daughter marry Paris, Juliet would not have found it necessary to fake her own death and Romeo would not have committed suicide.

Which minor character is most responsible for Romeo and Juliet's deaths?

Friar Lawrence is probably the most responsible for the deaths of Romeo and Juliet.

Friar Lawrence is known to be an alchemist by the herbs he is collecting. He marries Romeo and Juliet in secret. He devises a plan for Juliet to feign death and be buried in the Capulets' tomb.

Friar Lawrence sends his servant to tell Romeo what the plan is and what to do about it.  The problem is that Romeo did not get the message.

Friar Lawrence could have prevented Juliet's death if he had stayed at the tomb after Romeo and Paris were killed, but he ran off leaving Juliet alone to awaken to Paris, her dead fiance, and Romeo, her dead husband.