This depends entirely on the council's standing orders, which should set out how motions from councillors are to be treated by the proper officer (normally the clerk). Six days could be a bit tight. The clerk should really cooperate with councillors to get items on to the agenda, or to give feedback as to why they are not or when they will be.
These are typical standing order provisions:
a. A motion shall relate to the responsibilities of the meeting which it is tabled for and in any event shall relate to the performance of the council’s statutory functions, powers and obligations or an issue which specifically affects the council’s area or its residents.
b. In accordance with standing order 3(b)(iii) above, no motion may be moved at a meeting unless it is included in the agenda and the mover has given written notice of its wording to the Council’s Proper Officer at least seven clear days before the next meeting.
c. The Proper Officer may, before including a motion in the agenda received in accordance with standing order 4(a) above, correct obvious grammatical or typographical errors in the wording of the motion.
d. If the Proper Officer considers the wording of a motion received in accordance with standing order 4(a) above is not clear in meaning, the motion shall be rejected until the mover of the motion resubmits it in writing to the Proper Officer in clear and certain language at least seven clear days before the meeting.
e. If the wording or nature of a proposed motion is considered unlawful or improper, the Proper Officer shall consult with the Chairman of the forthcoming meeting or, as the case may be, the Councillors who have convened the meeting, to consider whether the motion shall be included or rejected in the agenda.
f. Having consulted the Chairman or councillors pursuant to standing order 4(d) above, the decision of the Proper Officer as to whether or not to include the motion in the agenda shall be final.
g. Notice of every motion received in accordance with the Council’s standing orders shall be filed and be available for inspection by all councillors.
h. Every motion rejected in accordance with the Council’s standing orders shall be duly recorded by the Proper Officer giving reasons for its rejection and the records shall be available for inspection by all councillors.
i. Every motion and resolution shall relate to the Council’s statutory functions, powers and lawful obligations or shall relate to an issue which specifically affects the Council’s area or its residents.