PH Dropping

does your water go through a softner first and if so can you get non-softened water? Test your KH and GH. I don't know why it would come out of the tap high then drop but I would guess that you have a KH of 0 in the tank. This can be adjusted with baking soda using this calculator. I keep my cichlids around 12-15 degrees of hardness KH. Of course it depends on what species you are keeping.

http://dataguru.org/misc/aquarium/calKH.asp

is that 12 kh or gh?

hmmm. KH is carbonate hardness, which is what your ph buffer, which is the one to be concerned with with regards to controlling ph. I would get the kit to test for that. I think that the api test you get at the big box stores includes both the gh and the kh test.

alternately, you could do the shotgun approach and treat without testing. You could put PH 7.0, .2, or whatever value you want in there, this puts in buffers and sets the ph for you, or you could by the buffer for what kinds of cichlids you have. Any of these products can quickly set ph and buffers up they way you need them. I prefer to measure and adjust with baking soda as it is much cheaper.

Here's a good article that explains why hardness is important when maintaining ph.

http://www.drhelm.com/aquarium/chemistry.html