I am not licensed in your state, but generally there is no constitutional right to counsel in a civil case. Some states have made exceptions, for example in actions to terminate parental rights. Your question is unclear as to whether this is an action to terminate rights, or an action to award custody to, say, an ex-spouse.
Since this legal action has already been filed, you should be able to find out if there is any special provision for you to get court-appointed counsel in this case by calling the Clerk of Court where this action was filed. Also, the local Bar Association of attorneys may be able to refer you to attorneys who take cases either free or on a reduced rate based on income. Some areas have volunteer lawyers foundations -- if so, Legal Aid should be able to refer you.
This communication does not establish an attorney-client relationship. This communication offers general information based on the limited facts set out in the question, and does not constitute the giving of legal advice. For specific legal advice, consult an attorney in your state who is knowledgeable in this area of law.
Unfortunately, the only circumstance that entitles one to a court-appointed attorney is the possibility of incarceration. So, no, the court will not appoint an attorney for you. Good luck to you!
This attorney can be contacted via email at firstname.lastname@example.org or via phone at 817.305.7170. The above answer does not constitute, and should not be construed as, legal advice.
As the two previous attorneys accurately pointed out, unfortunately you would not be eligible to receive a court appointed attorney in this instance. Other than being accused of a crime punishable by imprisonment, you are also entitled to receive a court-appointed attorney if someone is attempting to terminate your parental rights. Please note that terminating your rights is different than custody determinations. Best of luck!
**THIS ANSWER IS NOT INTENDED TO BE LEGAL ADVICE NOR FORM THE ATTORNEY/CLIENT RELATIONSHIP. YOU SHOULD SEEK THE COUNSEL OF AN ATTORNEY WITH THE SPECIFICS OF YOUR CASE**