Just tell them that you cannot have house guests and a newborn at the same time. You will resent them otherwise.
I'll tell you my dreadful imposition around birth of a child story (which still affects family relationships today).
When I was pregnant with DS2, H and I were living in a small 3 bedroom house far away from both our families. About 6 or so hours from my family and about 2.5 hours from H's. At the time, my stepfather was working abroad and my mum would spend most of her holidays (she's a teacher) out where he worked. She'd usually take my (27 year old at the time) sister with her (because my sister refused to get a job and leave home and look after herself. Important background info: I do not get on with my sister, who is a self-entitled and attention-seeking arsehole to put it mildly. H doesn't like her either, for the same reasons as me.
So, DS2 was due in early August and my mum planned to fly back towards the end of August to see him. He was, of course, 2 weeks late. In mid July she phoned me to tell me that my sister wanted to come and stay with us for 6 weeks spanning both before and after DS2's birth because she just loves babies so. H and i were supposed to feed her, do her washing, chauffeur her around in the car where she wanted to go, etc during all this time and she was (of course) to contribute nothing. I said no (not entirely politely, as I was taken aback by both my mum and my sister's sense of entitlement). I said she could come and visit for a day or so after the birth but no more.
My mum was very angry with me about this so between them my mum, my step-dad and my sister decided that they were going to impose my sister on us anyway. They booked a flight back for her with my mum and just decided that the pair of them were going to come and stay in our house for 2 weeks. I found out about this when H arrived back from picking my mum up at the airport with my sister in tow. A huge argument ensued because I was by that point overdue and in absolutely no mood for unwelcome house guests (and neither was H). My mum was incredibly nasty to me and said a great many things that now mean that I will never trust her or be close to her again. She was difficult anyway, but she made it clear that she thinks she is much more important than anything else and that I should just do what she wants all the time.
Her behaviour also made me very ill. I was having a horrible pregnancy and had been signed off work early and really, really did not need any more stress. But, my mum and sister clearly didn't (and don't) care about anyone other than themselves. They've made it clear that they are only interested in me insofar as they can get access to my children. Ironically, this means they get almost no access to my children because H and I don't want to see them.
H threw them out of the house and they went to stay at a local hotel. They then insisted on making sure that I got no time to spend with DS1 at all before DS2 arrived (and both H and I were too exhausted to fight). Poor DS1 felt he had to go with the too, but I know he wanted to just curl up with me and watch DVDs etc. Then, when I finally went in to labour, my mum (who was supposed to be looking after DS1 while H and I were at the hospital) wouldn't answer her phone so we had to call the PILs who drove up to us so that we could go to hospital. My waters has broken but the hospital sent me home because labour wasn't progressing with instructions about having to return by a certain time the next day. My mum came to the house that morning and went absolutely mental (actual screaming fit) when she saw FIL in the house.
After 36 hours in labour, I had DS2 and they forced me to stay in hospital over night because he was an instrumental delivery (although their doing so actually prevented me from getting any pain killers and delayed DS2 seeing a doctor by 24 hours because I had to be in the worst maternity unit in the country). Once I came home and was settled, my mum and sister visited to see DS2 for about 10 minutes and then left (having barely acknowledged either H or I).
The experience (as you'd expect) very much colours the relationship that I have with my family now. I absolutely keep them at arms length (indeed, H and I are having serious problems but there is absolutely no way I'd mention anything about it to my family; I probably wouldn't tell them directly if we got divorced). H loathes my mother (who essentially tried to make the birth of his child all about her and made everyone really miserable). The PILs think she's completely unhinged too (which is fair enough). My mum seems to think that her and my sister are 'all I've got', but frankly I'd rather having nothing than people who are perfectly happy to do me and my family great damage. I had to cut my dad out after DS1 was born as I didn't want his even more toxic influence, but I've had to accept that my entire family is toxic and contact with any of them should be minimised.
My sister is now pregnant and I hope she has as horrible a pregnancy and broth experience as she and my mother gave me. Not that she's learn any lessons from that.
I'm assuming that your PILs are not awful people, but unwanted house guests at the end of pregnancy/with a newborn are a recipe for disaster.