Does anyone know of any English speaking carers. There is a wheelchair/bedbound old English man who needs care. His wife can just about cope during the day but needs some respite at night.

There have been a lot of problems with local carers as the gentleman cannot communicate his needs, and this is why an English speaking carer is needed.
Does anyone know of any English speaking carers in Kunming?

I do not know but you MIGHT be able to find one by asking at one of the large hospitals in Kunming - Richland, say, which claims to be 'international', and definitely has English-speaking medical staff.

I know that such carers are available for inpatients at KM No. 2 Hospital, but finding an English-speaking one there would be a bit difficult.

Richland has a foreign nurse on their website. If you click on this site where they advertise, their is a group picture of nurses and one of them is a foreigner. Maybe she can help you.

Few years ago one of the local government sponsored hospitals in Kunming had two nursing students from my home country interning for a year or so.

This is probably more common, than having foreign nurses permamently on payroll.

Also I imagine that employed English speaking nurses (even Chinese nationals) often have to be on standby for their employers in case a foreigner with emergency shows up. Such may conflict with being available for this foreign person.

I would contact a nursing school or something like that, and ask if they have any (semi) English speakers who want extra cash -

combined with practical training in both English and their profession. Because this would be during evenings, it may fit their school schedule.

You also might try inquiring at Grace Medical Services (see gokunming listings).