Only institution that offers part-time studies that I know of is UNISA. Unisa now requires students to complete 8 modules preferably over 2 years. Studying here requires a degree of conscientiousness. These are internationally recognised but as with any immigrant requires evaluation by the professional bodies of the country you enter into.
To be a psychometrist one needs to obtain a BPsych degree or obtain Bpsych equivalency (only if you already have an Honour's degree) from an institution offering such a service where you complete a 960 hour internship at a recognised site. Unisa used to offer this but 2012 was the last year students could do their internships.
To be a counselling or clinical psychologist you have to obtain your Master's degree so you would need an Honour's degree to apply. The selection process is highly competitive; you need good marks (especially research), volunteer or work experience in the field of psychology, be emotionally mature and have good references. Universities can only accomodate a few students a year. If this is really what you want you'll have to be committed to working hard and always have a plan B is you are not accepted.
Good Luck with your studies!