There are many Career oriented courses offered in Mumbai but here you have not clearly mentioned that in which field you want me to give you the list. There are many types Career oriented courses after 10th or 12th or graduation. You have not even clearly mentioned about the field in which you want to pursue your career. Here I am listing the different fields in which you can make your career:

Food Science and Quality Control
Clinical Nutrition and Dietetics
Mass Communication and Video Production
Visual Arts
Still Photography and Audio Production
Instrumentation*
International Business
Jewellery Designing
French
German
Fashion Designing
Web Technology & Web Designing
Tourism and Airline Management
Remote Sensing
Kathak
Counselling & Guidance
Retail Management
Tax Procedure & Tax Planning
Banking, Insurance & Equity Services
Tabla
Gemology
Functional Accountancy
Event Management
Research Methodology
Radio Programme Production
Vocal Music
Instrumental Music
Folk Dance
Intellectual Property Rights and Patents
Early Childhood Care and Education
CCNA (CISCO Certified Network Administrator)
Integrated CAD and Graphic Designing
Patent Law and Practice (Certificate only-One Semester Course)
ICAI Certified Certificate in Accounting Technicians
Trademarks, Geographical Indicators and Domain Name
Dancing
News Anchoring
Radio Jockeying
Modelling
Vocal Music
Acting
Editing
Direction
Camera
Script Writing
Production
Broadcast Journalism
Media Management
Radio Programming & Production
Sound Recording & Designing
Graphics & Animation
Diploma in Film Arts & A/V Editing
Diploma in Animation including 2D & 3D Effects
Diploma in Print Media Journalism & Communications
Camera & Lighting Courses
Diploma in Filmmaking & Digital Video Production

Some of the institutes that conduct course the above mentioned courses:

Abdul Ahmed Garib Polytechnic College
Air Hostess Academy
Arts & Crafts Education Society
Bhavan Rajendra Prasad Institute of Communication & Management
Bombay College of Journalism
Frankfinn Institute of Air Hostess Training
Government Polytechnic
Indian Institute of Material Management
J.D. Institute of Fashion Technology
Mumbai College of Hotel Management
NYSS Shreeram Polytechnic
Padmashree Dr. D.Y. Patil University
V.A. Institute of Management & Professional Studies
Shri Bhagubhai Mafatlal Polytechnic
University of Mumbai
Vidya Prasarak Mandal College of Polytechnic
Global College Of Vocation
Kala Vidya Mandir Institute of Technology