The Farm Assist cuts in the Budget have been strongly criticised by both the IFA and opposition parties.
IFA president John Bryan said the decision to change the qualifying criteria for Farm Assist would hit the most vulnerable low-income farmers.
Mr Bryan said the new guidelines for Farm Assist could cost a married farmer with two children close to €2,500 a year.
"In many cases, these farmers will also take the hit on other farm schemes, which underlines the disproportionate and unfair nature of what the minister has done," he said.
The cuts to Farm Assist, which are estimated to deliver savings of €4m, have also been slammed by Sinn Fein.
Sinn Fein's agriculture spokesman, Martin Ferris, said the changes to the scheme would cost the most vulnerable farm families up to €40 per week.
"There are around 11,000 farmers on the scheme and around 70pc of them are in western counties where low-income farm households also avail of the threatened Disadvantaged Area Scheme which likewise contributes a small but essential element to family farm incomes," Deputy Ferris said.
"It is therefore vital that the scheme is maintained as it is as the proposed cuts would consign people in an already difficult situation to one that will be much worse."
However, Minister Coveney defended the cuts to the Farm Assist scheme, despite the equivalent payment to fishermen remaining unchanged.
"I take responsibility for the Farm Assist cuts because they were made by my Government. But Farm Assist wasn't the only one that was targeted.
"There were no easy options left in terms of welfare budget cuts since this was the sixth budget in a row of cuts," Minister Coveney told farmers at last week's ICSA AGM in Dublin.
Meanwhile, the IFA said it would continue lobbying Government ministers and TDs in an effort to get the farm sector Budget cuts reversed.
Yesterday, farmer protesters targeted Taoiseach Enda Kenny's constituency office in Castlebar, Co Mayo.
Similar protests were held in a number of locations across the country over the weekend. Mr Bryan said cuts to schemes such as the Suckler Cow Welfare Scheme, the Disadvantaged Area Scheme, the Sheep Grassland Scheme and Farm Assist would slash the incomes of thousands of farm families.
"The cuts by the Minister for Agriculture Simon Coveney to farm schemes have delivered a hammer blow to all farmers, and especially the low-income livestock sector," Mr Bryan said.
"Following a number of similar protests over the weekend, we expect the TDs to bring the message back to Minister Coveney, as he is responsible for the unfair targeting of farmers who rely heavily on farm schemes," he added.