It often depends on the school. Usually I see the MSCP if it is indeed a Masters of Science. Much like the common MACP, however in that case it is Masters of Arts instead on science. It can cause confusion from school to school but overall the answer will depend where you go.
MMHC
M.S. in Ed.
Master of Science in Mechanical Engineering
The Master of Education abbreviation - depending on the country - can be an M.Ed., MAEd., or Ed.M.
There is no specific abbreviation for a MA in counseling unless you have the marriage, child, family MA and that would MMCF. A MA or MS is just that and you normally don't use it after your name unless it is a professsional format.
Like most MS degrees, the MS in counseling does not require the completion of a master degree thesis. Also known as an acronym.
Within the United States there are only a few master's degrees that are very specific to ones major. For example, a master's in social work (MSW), a master of business administration (MBA), etc. Personally I have never seen an abbreviation particular to a masters in counseling. In general, the master's degrees fall into one of two categories. Either a master of arts, or master in science from which many specific programs of study fall. Thus, the abbreviation would be dependent on the school where you achieved the degree, and the approach they preferred, either the M.A., or the M.S..
It is typically abbreviated as MLIS (Master of Library and Information Sciences, or Master of Library and Information Studies).
On an employee nametag, it means Master of Science in Nursing.
It depends on the specialty (behavioral science, counseling, school psychologist, etc.)
B.L.S., B.Lib., or B.L.I.S - Bachelor of Library Science. MLIS - Master of Library and Information Science.
The closest I can find is a MBiolSci - Master of Biological Science under the British abbreviation system.
The University of Phoenix does not offer any counseling degree programs online. They do offer Master of Science Counseling degrees in Phoenix, Tucson and Salt Lake City.