You can set up a rule to allow
httpd_t to read the type of file your logfiles are labeled with.
For example, if I want
httpd_t to be able to read
your_log_file_type_t, you create a policy module like this (out of the back of my head). Call it apache_read_logs.te and put it in an empty directory:
allow httpd_t your_log_dir_type_t:dir list_dir_perms;
read_files_pattern(httpd_t, your_log_dir_type, your_log_file_type)
read_lnk_files_pattern(httpd_t, your_log_dir_type, your_log_file_type)
httpd_t to read files labeled
your_log_file_type_t and search through directories labeled
your_log_dir_type_t. It uses macros for brevity. You can see how the macros look by downloading and examining the reference policy tarball.
Then, from the directory you created the file in, you run, as root:
# make -f /usr/share/selinux/devel/Makefile
# /usr/sbin/semodule -i apache_read_logs.pp
This assumes you have selinux-policy-devel and policycoreutils installed. Test this on a non-crucial machine first! I wrote this blind and haven't tested it myself!