How do you word this in a cover letter?

[NoClueNoDough]

The job is advertised at 100%. I'm currently a sahm to a child with SN and looking to return to work.
Ideally, I'd like to go back to work at 40% but this is seemingly impossible.
I think 50% would be manageable, especially if 10% of that could be wfh.
At a stretch, 60% might be doable (if DH would step up, not certain).

How can I incorporate this into my cover letter? I don't want to lie and imply I can do 100% to get an interview and then get kicked out of it! I've been told by the unemployment advisor to mention why I've been a sahm and only looking for part time work.

Owing to the additional care needs of my eldest, I am looking for a part-time position with a maximum (occupancy?) of 60%.
Owing to the additional care needs of my eldest, I am looking for a part-time position up to 60%.
Owing to the additional care needs of my eldest, I am looking for a part-time position (max. 60%).

Is there a more natural way of phrasing it?

I’d simply ask if they are prepared to consider a job share/part time application before I went through the hassle of completing an application.

I’d call the recruiter and have a chat to them.

What the previous poster said. Asking for a small reduction in FTE is one thing, but your ask is way too much. Just email and ask if they'd consider a job share applicant. Don't apply till they say they would. Why are you being asked to apply for FT in the first place though?

Because there is nothing in my field that is ever advertised part time.
This job fits my profile exactly, and is honestly just what I'm looking for. It would also be a job that is ideal to split. But I cannot commit to 100%

Agree, contact them to discuss job share. There may be other potential candidates looking to do the same.