This is easier to achieve than first appears - especially if you can fence an area off.
To begin with the dogs are allowed only in this area until they have toileted. You will have to monitor this for some time and it is really effective if you attach a word to the action - I use, "Busy busy." But you could spend many fun hours deciding on your own phrase. Please remember that there may be times you will have to say this phrase in front of guests or in public before making your final choice!!! So as soon as you put the dogs into the fenced area you say, "Busy busy," or whatever appropriate (hopefully) phrase you have chosen. The dogs, of course have no idea what you are implying and your neighbours will be sniggering behind the hedges...
You continue to say your chosen phrase until one of the dog performs at which point you lose the plot totally and go mad squealing, "Good boy/girl (delete as appropriate), busy girl/boy, busy busy girl/boy!" (Your neighbours will have invited their friends around by now.)
You let the dog that has been "busy" out of the fenced area with lots of praise and possibly a treat and continue to encourage the other one to perform.
Only allow ten minutes maximum for toileting, if it doesn't happen then dogs go back inside without any free run of the garden and no walk or car trip.
Keep to your usual schedule of toilet breaks - and also use the fenced area before walks and car trips.
If there are mistakes out of the fenced area still praise the dog using the chosen phrase to reinforce the praise with the action.
Small note - when waiting for dogs to perform try to avoid prolonged staring or eye contact and try to pick up a pattern in what time of day they need to poop so that you can use the fenced in area to greater effect - only put them there if you know they are due one!!!!
By the time the dogs are trained you will either have neighbours that avoid you with worried expressions on their faces or you will get invited to every party in the district for novelty value!!!