The party’s finance secretary Murdo Fraser said the minority SNP administration could unlock talks for a pro-business budget but must “dump indyref2” first.
A government source said given the Brexit situation the Tories are in no position to dictate terms.
Setting out his proposals at Edinburgh Airport, Mr Fraser said they included a cut in Air Passenger Duty (APD) and increased support for high street retailers.
The Scottish Government wants to replace the duty with a cheaper alternative which was voted through at Holyrood in June 2017.
However, the rates have not been decided and the plan is snared in a legal stand off between the Scottish and UK governments over European state aid rules.
The Scottish Green Party, whose helped last year’s Budget get through parliament, oppose the tax cut.
Mr Fraser said: “Last year’s Budget deal between the SNP and the Greens was bad for jobs and bad for Scotland’s economy.
“We do not want to see a repeat this year. So today the Scottish Conservatives are making it clear that if the SNP puts the needs of Scotland’s economy first, it could win support from us.
“Central to that is the need for the SNP to dump its plans for a second independence referendum in this parliament.
“The message to the SNP is clear: dump Indyref2 and let’s talk.”
A Scottish Government source said: “We will engage constructively with those who, like us, have a genuine interest in passing a budget to fund Scotland’s schools, hospitals and other vital public services.
“But the Tories - who are dragging Scotland ever closer to the cliff edge of a catastrophic no-deal Brexit - are in no position to try and lay down the law to anyone.”
Scottish Greens co-convener Patrick Harvie said his party has used last year’s budget talks to stop the worst of council cuts and influence income tax policy.
He said: “This is a tiresome bit of attention seeking from sidelined Tories who clearly have no interest in influencing the Scotland’s budget choices.
“Tax cuts for the rich, tax cuts for the already-undertaxed aviation industry and wealthy frequent fliers, and the spurious notion that independence is a budget issue are all non-starters and they know it.”
Meanwhile, the aviation industry called for action to resolve the legal impasse on APD, with Glasgow, Aberdeen and Edinburgh airports saying it is “costing Scotland connectivity and the economic benefit and jobs it brings with it”.
Tim Alderslade, chief executive of Airlines UK, added: “Aviation in Scotland is crying out for this cut and it is now up to both governments to bang some heads together and put an end to this legal wrangling.”