Are Christians not permitted to have sex with wife when she's on her period?
Acts 15:29 refers back to Leviticus 17 and 18, where the laws which apply to Gentiles ("strangers"/"alien") who have chosen to live amongst the Covenant people are given. In other words not all the ceremonial laws applied to the Gentiles living amongst the Jews.
Those laws which they should seek to keep can be seen to parallel the laws in Acts 15:29 thus:-
They should not eat things offered to idols, Lev 17:1-9;
They should avoid eating blood, Lev 17:10-14;
They should avoid eating things strangled or dying in an
"unapproved" way, Lev 17:15-16 (- it seems that, amongst the gentiles in NT times, strangulation was a way of killing animals that were going to be eaten);
They should not commit fornication, Lev 18:6-26.
Most of these laws are ceremonial. As such they are not forever binding on Christians: a Christian needs only to observe them when in the company of Jews so as not to cause offence to Jews, for instance when a Jew has become a Christian, and is thus in the same fellowship for worship. (For more on this see: Does Acts 15:21 assume new believers would learn and follow the law from synagogues on sabbath? ).
Some of the laws required in Acts 15:29, especially relating to fornication, are moral. The point here is that Gentiles would need instruction in what is moral and what is not from God's word, especially from Leviticus 18.
So, as for permitting sexual intercourse when one's wife is having a period, this is a ceremonial law not a moral law (unless someone can show otherwise) and as such it is finished along with all the other ceremonial laws. If a Gentile Christian were to break this OT ceremonial law it would not be an activity which any Jew would be aware of; it would be a purely private matter between the husband and his wife, so it was not actually covered in Acts 15:29 at all.
What the early Christians are being asked to respect in Acts 15 is the consciences of Jewish believers and other Jews who might become interested in the Gospel, so as not to be a stumbling block to them. So outward behaviour visible to the Jews in their company is what the verse is talking about.
The verse which sums up the reason for Acts 15:29 is:
"For though I am free from all, I have made myself a servant to all, that I might win the more; and to the Jews I became as a Jew, that I might win Jews; to those who are under the law, (I became) as under the law, that I might win those who are under the law... I have become all things to all men, that I might by all means save some. Now this I do for the gospel's sake, that I may be partaker of it with you." 1 Corinthians 9:19-23.
Christians are not under any ceremonial laws, but the Christian has a moral duty not to be a stumbling block to other people whose consciences may be differently educated. The reason is so that the propagation of the Gospel is not hindered: a Christian must submit to the consciences of others so he can be more effective as an evangelist.
To give a simple example, if you were to invite a Jew to your house for a meal would you give them pork? Of course not. Would you eat pork when you are alone with your family? There would be no Biblical reason to avoid pork in the privacy of your own family.
The reasoning is applied to the Jews but the principle applies equally to other groups such as Muslims and others. The Christian must respect their consciences when in their company also, that the success of the Gospel be not hindered.
Post Script:
There is one more troublesome thought: why give a command to avoid fornication to the Gentiles in Acts 15 at all? After all, should it not be obvious from the whole New Testament that the gentiles should avoid fornication, and that, not just to avoid offending any Jews but because it is morally right at all times to avoid fornication? Surely the answer is that we all tend to learn what is right and what is wrong from the culture around us; and where the Bible is not taught the conscience does not always recognise what is sinful. The newly converted gentiles in the NT era needed to learn the definition of fornication that the Jews had... they needed to learn and obey Leviticus 18:6-26. (We still do.)