My guess is that cost is probably your main issue as far as why you don't just replace them with a new, single router. That would be by far, the best way to go for your situation.
1. If your ISP offers 2 dynamic IP addresses (i know Time Warner does, and i think it might be common for most cable company ISP's) then you could connect a switch to the cable modem (note: plugging 2 computers in this way is a good way to test to see if they both get an IP address) and then plug both wireless routers into the switch. Benefit: no double NAT-ing, or "misfires" of internet request returns.
No matter what you do, make sure that you set the Wireless Channel at least 2 channels (1 & 3, etc) apart from each other, but make sure that you don't set your channel the same as any other nearby networks for either router.
2. If you only have 1 IP from your ISP (usually DSL or long-range wireless providers), then plug in the reliable router to the modem/DSL router first, then the faster/less reliable router second. Same channel rules still apple so they don't interfere. You would need to make sure that whatever Subnet (not subnet mask) the 1st router uses doesn't match the second.
Example:
1st router:
-WAN/Uplink/Internet port plugged into modem/DSL router
-LAN port/wireless as follows
Internal IP: 192.168.0.1
subnet mask: 255.255.255.0
DHCP pool: 192.168.0.50 to .254
2nd router:
-Wan uplink port into LAN port of 1st router
-LAN port/wireless as follows
Interla IP: 192.168.1.1
subnet mask 255.255.255.0
DHCP pool: 192.168.1.50 to .254
in this way, the subnets are different, double-NAT isn't usually an issue.
Good luck!