There aren't very many jobs where all you do is program and troubleshoot PLCs. You didn't say what your qualifications are other than to indicate an interest in PLCs.
A PLC is one of many tools used in manufacturing automation. If you have some basic mechanical and electrical skills as well as an understanding of the components involved in automation, you could apply for a maintenance position in a manufacturing facility where you may get a chance to troubleshoot and make modifications to existing PLC programs. If you display an aptitude for PLC programming, you may be given the opportunity to to create a PLC-based control system from scratch.
You could also apply for a job with an OEM. You may find that the only PLC-related openings available to someone without an engineering degree are in field service.
If you already have your engineering degree, then there are more options available to you. You can apply for jobs in the engineering departments at manufacturing facilities or OEMs.