In many Baptist churches, women are not permitted to be deacons, although that is not a uniform view by any means. For clarification, when I am talking about deacons, I am talking about persons who serve the church and community as designated representatives of the congregation, administrating and organizing the distribution of resources and services to the needly, hospital and home visitation to the sick and infirm, and general care of the congregation. They are not a ruling body, but they are wise persons that the church often goes to for counsel, both individually and corporately.
Yes, although no one "is allowed" to be a deacon at our church, they must be asked. In our congregation, men and women are nominated by input from the congregation by optional secret ballots, and then an ordination committee reviews nominations and prayfully recommends ordination to the church for those persons whose lifestyle, acts of service, and concern for the practical needs of the congregation are amply evident. We generally look for people who are already serving others according to their giftedness, and then affirm them in that calling through ordination and official empowerment to continue their work.
We seek both men and women to serve in this role because that appears to be a biblical standard. Among many other women who served in ministry positions in the New Testament churches, we know that Phoebe was a deacon and a minister (Romans 16:1-2) and was entrusted by Paul to carry the letter to the churches of Rome.
Our church began ordaining women to the deacon ministry back in the 1970s after a careful study of the scriptures by the congregation and leadership. Well over 40 years later, the church has benefited tremendously from having women officially serving in this role.