There is not, in my opinion, any other way of trying to ensure inmates' rights that is likely to be as effective as lawsuits. This is because other avenues for ensuring these rights rely on the elected branches of government, which are likely to be less sympathetic towards inmates.
The elected branches of government are likely to be very unsympathetic to appeals for inmates' rights. Convicted prisoners are not a popular group and so there is little political benefit to voting to protect their rights. At the same time, protecting inmates' rights typically involves money (for example, money spent on new prisons to relieve overcrowding). There is likely to be little sympathy for spending money to help a hated group of people.
If the elected branches are not likely to ensure inmates' rights, then lawsuits would seem to be the only real alternative.