Sir Paul, founder of the Marriage Foundation think-tank, said the idea would be an acknowledgement that stable families ultimately save the taxpayer money.
He also said that couples who choose to cohabit rather than getting married should not have children.
Sir Paul stepped down from the judiciary to concentrate on the think-tank and amid controversy over his public stance in favour of marriage.
His latest comments came during a debate organised jointly by his foundation and The Sunday Times.
Dismissing the relatively small tax break for married couples offered by the Coalition as inadequate, he said: “Why does the Government not support people by incentivising sticking it out?
“Increasing the tax allowance at five years, 10 years and so on would do two things – it would make clear staying together does not cost the state a penny while splitting up does and it would send a message to couples to stay together.”
Research published previously by Sir Paul’s foundation concluded that children whose parents were not married were twice as likely to suffer a family break-up as those whose parents were married.
Almost half of newborn babies in England and Wales now have unmarried parents, according to official figures.