A slave who is a non-muslim living in the Islamic state is a dhimmi and can not be forced to accept Islam. A dhimmi slave however does not pay Jizyah, as Jizyah is only due from adult, sane, free, males.
أن يكون كافرا فيجبره سيده على الإسلام، فلا يجب على الرقيق طاعته في ذلك لأنه لا إكراه في الدين. واستثنى الحليمي من الشافعية أن تكون كافرة غير كتابية ويرغب سيدها في الاستمتاع بها، فيجبرها على الإسلام لتحل له، فرأى الحليمي جواز ذلك لإزالة المانع من الوطء، قاسه على جواز إجبارها على إزالة النجاسة وغسل الحيض. والصحيح عند الشافعية خلاف ذلك.
If the slave is a disbeliever and his master coerces him to accept Islam, then it is not obligatory on the slave to obey him in that, for there is no compulsion in religion. And al-Halimi from the Shafi'is has made an exception for a disbelieving woman from a religion other than the people of the book, that when her master wishes to satisfy his desire with her then he can coerce her towards Islam so that she will become lawful for him, and al-Halimi has compared it with the legality of removing other obstacles to sexual intercourse such as coercing her to remove ritual impurities or taking the bath for menstruation. And the correct saying of the Shafi'is is against that.
— Encyclopedia of Islamic Jurisprudence