The information I've seen on the subject suggests that Manufacturing Plants make [capacity]/100 size of components and Construction Yards will install floor([construction speed]/100) components every six in-game days.
I have not personally tested that thoroughly enough to vouch for its accuracy. I can, however, tell you that when I tested two shipyard designs, one with 10 of each plant and 30 construction yards and the other with one of each plant and 30 construction yards, and had both shipyards build 30 capital ships of the design that the computer had generated for my empire at the time (new game, tech level 7 ackdarian empire), both shipyards appeared to be building the ships at the same rate (based on checking the change in project completion percentage for each construction yard in both shipyards at intervals during the project; the test was ended prior to completion of construction as the planet over which the shipyards were built ran out of resources when construction of the sixty capital ships was roughly 50% complete). This test result is not inconsistent with the hypothesis given above; at tech 7, a station with 3 manufacturing plants and 30 construction yards would be able to construct ships at something close to maximum rate as long as the average size per component used in the designs of the ships under construction was no greater than 15. You might run into delays due to insufficient plant capacity while trying to build a fleet of carriers, but you'd probably be good to go for just about anything else.
Under the assumption that the hypothesis given above is correct, the ideal ratio of construction yards to manufacturing plants and the ideal ratio of weapons plants to energy plants to high tech plants will be dependent upon the designs of the ships that you are building. Regardless, if the hypothesis is correct, I would expect that four of each plant will in general be more than sufficient for seventy construction yards to work at maximum rate or something very close to it, as the total manufacturing capacity is such that your construction yards shouldn't be able to install components more quickly than the plants can build them unless the average component size on the ships being built is greater than 17-25 (depending on construction/manufacturing tech).
The information that I've seen can be found here.