The Independent Lothians MSP said she was ready to back the SNP's budget in the Scottish Parliament if she got a commitment to the new money.
She said such a scheme would improve the city's fabric and help make it more attractive for visitors and businesses as well as providing work and training and preserving important skills.
Ms MacDonald said she could not put a sum on how much she would be seeking until she held detailed talks with council chiefs.
The arithmetic in the parliament means her vote could prove crucial when Finance Secretary John Swinney asks MSPs to back his spending plans within the next few weeks.
Last year, the budget was defeated on the casting vote of the presiding officer.There had to be a fresh round of talks with the opposition parties before it was brought back and approved.
Ms MacDonald said: "I have told them I will be asking for something this time and I make no apology because I think the position of Edinburgh is now beginning to be seen to be very difficult indeed and the city is getting a shabby look to it.
"I want a scheme where they can take on stonecraft apprentices and building industry apprentices but with a specialism of working on old buildings in Edinburgh so they can have a programme for renovating the stairwells and common fabric of Edinburgh's housing stock. It would maintain the housing stock, give people proper jobs and raise the skill level."
She said areas which would benefit could include Leith, Leith Walk, Gorgie/Dalry and part of the south side, and streets which disrupted by tramworks might be put at the top of the list.
"While the council is recruiting apprentices, they could carry out a quick consultation to ask people living in the areas most disrupted if they are interested."
Two years ago, when the SNP presented its first budget at Holyrood, Ms MacDonald successfully argued for the creation of a Capital City Supplement, a new annual budget line which recognises the special demands Edinburgh faces as the capital city, but she made clear her call for stonemason investment was separate.
"The Capital City Supplement is an ongoing stream of revenue. What I'm asking for is something additional to recognise there is something of an emergency situation in Edinburgh. There is a lot of stonework in tenemental property that is needing to be fixed before it becomes unfixable, and I imagine the sustained frost will have attacked a lot of that fabric.
"The government is willing to try innovative ways to try and get people back into work. What I'm looking for is not just getting them into work but getting people trained so there is an added value."