Visa dependent

Really?   I don't know if you are in Bahrain or not but you need to research better or understand the cultural norms here.  There are threads on this forum discussing issues similar to yours.   The search icon is your friend for this.

Simply in the current situation:

1) You CANNOT sponsor your boyfriend (Bahrain law doesn't recognise that relationship, being a Muslim country).  And you CANNOT sponsor husband either.  See the comment from LMRA below on that.  To my knowledge, the only exception to this that I have heard about is applied only in the case of financial services / banking industry etc.

http://lmra.bh/portal/en/faq/question/37

2) You CAN sponsor your child. But you would need to have a birth certificate with father's name on it, custody documents in your favour or notarised attested NOC from Father as well as a minimum salary of 400 BD registered at SIO

The options are:

1) You get married. Get an attested marriage certificate and birth certificate.  But you still cannot sponsor husband unless your employer gives him a work permit of his own.  This is only done by companies for very senior female employees to get them to move to Bahrain (why would they waste their work permit on someone who won't work for them unless they really wanted the wife to be here)
2) You get married. Your boyfriend gets a job here and moves on his own visa.  Sponsoring child is not an issue in this case
3) You don't get married. Your boyfriend gets a job here and moves on his own visa.  Either you or him sponsor the child but with all the relevant documents i.e. custody and so on