Scores of motorists are thought to have been caught out by the recently introduced restrictions when parking at Arboretum Place, next to the popular tourist attraction.
They are being slapped with fines despite having bought a parking ticket because they have used the wrong machine.
One machine charges a minimum of 3 for one side of the road, where people can park for a minimum of three hours. On the other side of the road, another machine allows people to buy tickets for up to four hours with no minimum stay restrictions.
Council chiefs were today urged to scrap the confusing system or improve signs telling motorists what to do.
Sasha Paul 28, was given a fine when visiting the Botanics with nine-month-old daughter Emily. Ms Paul, a teacher from Balerno, had parked on Arboretum Place and found a queue at the meter next to her car.
Because it was raining and she was worried about her daughter catching a cold, she ran over to buy a two-hour ticket at the other side of the road.
When she returned about an hour-and-a-half later, she had been given a fine.
Her husband Craig, 37, said: "We're not people who get a lot of parking tickets and that's why it's so frustrating. It seems like a sneaky way of catching people out.
"She couldn't believe she had a ticket because she thought she still had half an hour to go. How were we meant to know we weren't meant to buy a ticket from the other side of the road?"
Mrs Paul also claimed in her appeal letter that a warden told them "hundreds of people get caught out here".
The new regulations for the street came into force in November, meaning two sides of the road have different rules.
Alan Gullard, 70, said he has always paid to park on Arboretum Place for an hour or two during regular visits to the Botanics, but earlier this month found a parking fine when he returned to his car despite not running over the time he paid for.
Mr Gullard, who lives in Corstorphine and was visiting the Botanics with his wife and grandchild, said: "What angered me was that there was no visible notices to say that the charging system had changed."
He added that several other cars on the street also had tickets.
Councillor Lesley Hinds, who represents the Inverleith ward, said: "I will be asking the director of city development to change this. If they can't, they need to put notices up that make the rules clear.
"It looks like the wardens on mopeds are coming to this street to make up their numbers because they know they will catch people out."
The city council said that parking instructions and fees are printed on both machines, while there are arrow signs at bays pointing to which ticket machine the public should use.
In relation to Mrs Paul's ticket, a council spokeswoman said: "The ticket was issued correctly in this case."