But their meetings may be doomed. The police are on to them - not for the drugs, though. It is the telephone cards. More about this later.
This unlicensed gathering takes place barely 100 yards from Omotes ando-dori, one of Tokyo's smartest boulevards full of boutiques and cafes and people who flit from one to the other, busy looking rich. The impromptu souk, by contrast, has few pretensions, catering to the simple tastes of labourers who are far from home, trying to save as much of their earnings as they can in the world's most expensive consumer society.
Thousands of Iranians have come to find work, using tourist visas to get in and then enlisting for the dirty, dangerous jobs that the Japanese no longer care to do. Employers are keen to use them as cheap labour, but they have no health insurance or legal protection against exploitation.
In the market the loudest stallkeepers are the kebab sellers, touting their skewers of meat as soon as they are cooked through on the charcoal grills. Four skewers of beef and a loaf of bread are the same price as a cup of coffee down the road.
Munching on their kebabs, the men sidle over to watch Iranian football on a television perched at an uncertain angle in the lower branches of a tree. One team appears to be playing uphill, but still manages to score a goal. Videos of matches and feature films have been sent over from Iran to Tokyo, where they are copied and sold, to while away the evening hours after a day in the sweatshop. Music tapes are also for sale, as are Iranian newspapers, days or even weeks old.
There is a man who sells Persian carpets - but he is almost like stage scenery. Buyers are more interested in the tracksuits and stone-washed denims that seem to have become standard leisurewear in much of the central Asian land mass. Several merchants walk around with fake leather jackets draped over their arms.
In one corner is an open-air barber's shop, where half a dozen practitioners have set up for business with folding chairs and scissors and combs. The ground is thick with dark locks of hair, shorn at a fraction of the price a Japanese hairdresser would charge.
The bazaar is crowded, and the men do not automatically move out of each other's way as a Japanese crowd manages to do without even thinking about it. They stand their ground, these Iranians, asserting a temporary claim to this corner of the park after a week out on the labour market where no one needs to remind them that they are working in Japan illegally. From the quieter corners drifts the sweet, tell-tale smell of hashish and there are a few discreet offers of the substance for sale.
This is all highly unusual for Tokyo, where ethnic diversity is hardly encouraged, cooking on an open fire without a permit is doubtless illegal, and smoking narcotics in public certainly is. For some young Japanese it has become a new thrill to wander between the stalls of tall, swarthy men haggling passionately with each other in a most un-Japanese fashion.
But this colourful little Tehran may be doomed - by a fake telephone-card racket run by Japanese gangsters, and the eagerness of some Iranians to make a few extra yen, even if it is on the fringes of the law.
The scam appears to have been quite clever. Japan's telephone company, NTT, authorises three firms to print telephone cards. These companies first make the plastic cards with their backing of a magnetic synthetic resin, which contains the coded amount of credits. The cards are then embossed with the name of the maker, the date of production and the NTT logo. The cards are registered with NTT and distributed for sale. But, according to the police, tens of thousands of cards have been disappearing from a manufacturer, before they are embossed with the NTT code. It seems that some cards are deemed to have been badly printed, marked for disposal and have turned up on the black market.
Police suspect that yakuza gangster syndicates are behind the scam. A number of Iranians have become involved in distributing these cards. This the police do not like. They can take the unlicensed merchandising and even turn a blind eye on the hashish. But the telephone card scam links back into the Japanese mainstream - a police swoop is imminent. The security of an Iranian home-from-home may be over.