Gardena is on of several timers on the market that will suit your requirements. Galcon is another. Quick question, I assume you are connecting to the tap directly and not through a small holding tank? If you are working with a tap timer options are limited but as Steephill says most controllers/timers, even tap timers will give you the ability to run minimum run times of 1 minute and alternate between days. If you consider a DC controller and link to a valve the control element changes completely as you can operate by the second and loop the times so they give a much wider variation on control.
Two links below might give you an idea of what is available;
In answer to your question about drippers - there are lots of options you can have. Industry standard is 2,4 or 8lph - generally these are fixed output. Compensating means the output will remain constant regardless of the input pressure, there are non compensating types. If I were in your position I would consider an adjustable type called a Shrubbler. Not an exact Dripper per say and not compensating (this one anyway) but it is adjustable from max flow 49lph/0.816lpm to minimum flow 0.037lpm at 2bar pressure or at 1bar pressure 0.025lpm compared to your 0.067lpm from a 4lph dripper. Have a look at this link on youtube;
Hope this helps