How Much To Pay For Respite?

Hi - My child aged 9 yrs has Aspergers.  They have very significant sleeping problems and generally difficult and challenging behaviour at home (very argumentative and strong-willed.) We are under PALMS. I am a single parent and we are struggling alot at the moment, no doubt because of the hols, but I have reached the decision that I do need to look into future respite.  I don't think that the local authority would help: We live in a very modest 2 bed house but I have a few savings, in lieu of any pension.  I was thinking of asking a couple of friends if they could help out by having my child to stay with them for perhaps 1-2 days a month.  My child's behaviour would probably be OK with them and they might not notice the sleeping difficulties for the first few times. My child is likely to just lay awake in bed until they become more settled and then the screaming might start. Any suggestions as to what I should pay? I am a Carer so don't have any income but I can't expect/hope for them to help me for free. Thank you.