to ask them to announce their intention to visit?

[MrsEames]

MIL turns up without letting us know prior. Usually at tea time after school or Saturday which is our lazy PJ/films/baking/craft day.

I find it really annoying because I like a bit of a warning that people are coming over. My own mother calls before coming,as do my sisters.

AIBU to ask her to phone first to make sure it is convinient?

Guests are generally invited to visit, not just turn up when it suits them. You have a choice, or rather you have a number of them. I favour not answering the door if you're not expecting someone but you could choose to say "Sorry, not now, we're doing X, Y or Z" or "We're just off out, you should have phoned first".

But you need to be prepared: whatever you do is likely to cause unhappiness. Either theirs or yours, you decide.

just tell her politely that you would prefer it if she rang first to make sure it was a suitable time to visit....and if she doesn't then just ignore the knocking on the door

YANBU, I've made it very clear to my MIL that I don't like unexpected guests and I have made her wait on the doorstep whilst I finish giving DD a bath before, bloody woman still hasn't learned so I just don't answer the door anymore