Staff in Jobcentres, banks, building societies and utility companies in England could also be trained to spot - and counsel - vulnerable people.
The ideas are raised in a consultation paper on suicide prevention.
The Samaritans said councils should have a mandatory responsibility to try to prevent suicides in their areas.
Some 4,400 people killed themselves in England in 2009.
Claire Wylie, head of policy and research at the Samaritans, told the BBC News website that many suicide attempts were made on impulse, so trying to restrict access to potentially lethal means was important.
"We know that people who are feeling suicidal are often very ambivalent about actually ending their lives," she said.
"If you can interrupt them at that moment you can prevent them going ahead."
Preventing deaths by jumping is a key aim of the consultation and it suggests a number of ways of doing that.
They include:
Overall, the number of suicides has steadily fallen in recent years, but the number of deaths on Britain's rail network had been rising until last year.
However, specialist training from Samaritans for rail staff was key to an 11% fall in 2010, according to the Rail Safety and Standards Board.
London Underground is also rolling out training to all of its staff after a pilot project at one station close to a psychiatric inpatient unit helped reduce suicides.
The government wants to see that sort of training given to a much wider range of people who come into contact with individuals who could be vulnerable because of their social or economic circumstances.
Jobcentre and benefit office staff, as well as employees in banks, building societies and utility firms are among those suggested in the consultation.
Ms Wylie said: "More training for all frontline staff is really important, but that needs investment and money is tight.
"In general, we really welcome the government's strategy, but there needs to be a lot more actual commitment to action.
"There's also an issue about local implementation because things like putting up signs and barriers depend on the individual local authority actually caring about suicide prevention.
"We would like to see a mandatory responsibility placed on local authorities to take this seriously."
The consultation closes on 11 October.

The 40-year-old 14-time major champion twice had back surgery during 15 months out before returning in December, when he tied for 15th at the 17-man Hero World Challenge.
Over the next five weeks he plays four full-field tournaments.
"That is a concern, no doubt about it, but I'm also looking forward to it. I've sat out long enough," Woods said.
"I've gone through some pretty tough lows. There were points when I didn't know whether I would swing a golf club again.
"But I do feel good about it. I just need to get out there and do it and see what happens."
Woods begins his 2017 season at the Farmers Insurance Open in San Diego, which begins on Thursday.
He will then play at the Dubai Desert Classic from 2-5 February, followed by the Genesis Open at Riviera from 16-19 February and the Honda Classic in Palm Beach Gardens from 23-26 February.
"I've got my body in a pretty good state where I feel I can handle that workload, but I've still got to go out there and do it," he added.
"Feeling good about it and doing it are two totally different things."
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The girl was forced into a vehicle in Bishop's Stortford at about 20:30 GMT on 16 February and dropped off near the town's railway station the following morning.
An E-fit image of the attacker has now been released.
Police said the attack had caused "concern within the community".
The girl was forced into a dark-coloured vehicle, thought to be a Land Rover, and taken to an unknown location, believed to be outside the county of Hertfordshire, where she was sexually assaulted.
Ch Insp Gerry McDonald of Hertfordshire Police said: "I believe local people hold the key to our investigation.
"This is an extremely serious matter and one which, understandably, has caused concern within the community.
"We have conducted a number of inquiries in the local area but would ask anyone who was around between the times mentioned and who has not yet spoken to police to contact us if you have any information which may assist our investigation.
"I would like to reiterate that this is an unusual incident and would reassure everyone that investigations into this incident are a priority."
Multi-storey car parks, bridges and tall buildings could be designed to make suicide more difficult, under government proposals to save lives.
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