The House of Lords will have to agree the suspensions before they come into force.
The recommendations follow investigations by the House of Lords commissioner for standards into allegations made by The Sunday Times and the BBC's 'Panorama' programme about three members of the Lords.
Laird, who is a fellow of the CIPR, was found to have breached the Lords' code of conduct by failing to "act always on his personal honour" in three respects: by demonstrating a clear willingness to negotiate an agreement to set up an all-party group in return for payment or reward in two separate incidents, and by demonstrating a clear willingness to negotiate an agreement that would involve providing parliamentary services in return for payment or reward.
Laird's appeal against the findings and the recommended sanction of four months was not upheld by the committee.
Mackenzie was found to have committed four breaches, including agreeing to set up an all-party group on behalf of a paying client and demonstrating a clear willingness to negotiate an agreement that would involve providing parliamentary services in return for payment or other reward. He was found in breach of rules regarding the use of the facilities of the House and in breach of the requirement for members to act always on their personal honour in relation to a single incident, a lunch held in the House of Lords found to have had the purpose of increasing business to Ivy Link, a commercial entity in which he had a financial interest.
Mackenzie appealed against the findings in relation to the first two breaches above, as well as the recommended sanction of six months, but his appeal was not upheld by the committee.
The third Lord against whom allegations were made, Lord Cunningham of Felling, was found not to have breached the code of conduct and not to have demonstrated a clear willingness to do so.