Councillor Graham Hinchey said the authority still faced a real terms cut to its budget despite its grant from the Welsh Government rising by 0.3%.
The authority is looking at increasing council tax by 3.7% and making cuts of £17m.
Costs for burials as well as births, deaths and marriage registration and school meals could all rise in 2017-18.
Along with the proposed cuts, £1.5m from reserves, £1.9m from school budgets and £4.4m from the planned increased in council tax would help make up the shortfall.
The cuts are smaller than 2015-16, when £32m in savings was proposed, and 2016-17, when the shortfall was £45m.
Proposals include:
Cardiff council saw its Welsh Government grant rise by 0.3% to £428m. The overall budget for 2017-18 is £578m.
Mr Hinchey, cabinet member for corporate services and performance, said: "The provisional settlement from Welsh Government is slightly more favourable than we bargained for.
"However, it is still a cut in real terms because of price and pay inflation."
The council is asking residents to share their views on the proposals in a consultation, which runs from 10 November to 11 December.
Cardiff council needs to find £25m to balance its books next year, the authority has said.