The Baby Bonus and School Kids Bonus should be streamlined and paid through the family tax benefits system, the Australian Council of Social Services (ACOSS) says.
The family payments need to better target low and middle income families, according to a pre-budget submission by ACOSS released on Friday.
"We cannot afford to have these kinds of bonuses paid at a flat rate to families or households, which in some cases have an income of $150,000," ACOSS CEO Cassandra Goldie said on Friday.
She said under the council's proposal, families would still receive the money but it would be paid as an increase to the Family Tax Benefit Part A to ensure it was best targeted to lower income families.
The baby bonus is $5000 but the federal government plans to cut it to $3000 for second and subsequent children.
The School Kids bonus meanwhile provides $410 for each child in primary school and $820-a-year for each high school student.
Dr Goldie said the council's proposed reform would be cost-neutral because the money would still be paid, just in a different way.
The single rate of Newstart Allowance also needs to be increased, ACOSS said.
"Increasing the abysmally low base rate of allowance payments by $50 a week is the single most important thing this government could do to lift more than one million people out of poverty," Dr Goldie said.
ACOSS estimates it would cost about $1.8 billion to increase the payment in 2014-15.
This could be funded by clamping down on higher-income households using private trusts and capital gains to avoid income tax payments.
The council is also proposing scrapping the health insurance rebate for `extras' cover, the Seniors and Pensioners Tax Offset and non-superannuation termination payments because they are "wasteful" measures.
ACOSS says it has found $6 billion in federal government savings.