食事中は携帯を置きなさいって英語でなんて言うの？

These are all simple instructions that convey the same message.You might even want to be a bit firm and say :
-If you don't put that phone away I will take it away from you
*This is a subtle threat to let your child know that there are repercussions.
-If you keep fidgeting with that phone I am going to take it away until you learn how to behave.
This is another firm way to make sure that he/she puts the phone away.

1. This is the logical approach. You ask for the phone to be put down because it will get messy.
2. Here you state that it is generally rude to use a phone while eating. Depending on the age of the child, this censure should trigger the reaction of putting down the phone.
3. You state that the child may get a stomach ache. This should be sufficient warning for the child to put down the phone.

Depending on the situation you may want to have this as a rule, and in that case you can say that it is not allowed.
Saying it is not allowed will mean that you do not have to continually ask them to put their phone away while eating, as they know this is a rule to to be followed at every meal.

NOT, AT THE TABLE! - this in a hard voice will tell the child that this is not allowed while at the table eating (assuming that you eat at the table). It will also set down rules of etiquette for the child. Personally this is what I would use.
Put your phone away at the table/while eating - this is ok as it will tell the child to put their phone away but may be the same problem tomorrow.
Put it away or I will! - This will tell the child that you are frustrated with them, and if they do not put it away, you will take it off them. (best choice)

These are two statements that can be used to tell a child to put their phone away when they are eating.

1. Please put your phone away until you have finished eating .
2. Eat first, and then you may use your phone.

1.No phones allowed at the dinner table.
2.No phones will be touched while we are eating.
3.I do not want to see a phone while we are eating.

*allowed=restricted
Sentence 1 means that phones are not allowed at the dinner table, or it means that it is banned.
Sentence 2 means no phone touching, means hands off the phones while eating.
Sentence 3 means that you do not want to see a phone while eating. so this is clearly indicating that a phone should not be taken out or used while eating.

You can say to them any of these questions. It depends on how you want to say it. The second question is a very demanding one.

Depending on the situation, but both will get the message across. Also, you can add please to the first one.