the library's online portal says it accepts renewals only if the IP is from the same state as the library

 

the VPNs i have tried don't offer an IP for my home state. 

 

is there some other method i can use?

you could order a VPS/VDS in that state, and use it as a SOCKS proxy.

or just google for "free socks proxy" adding your state name.

Are  proxydocker.com  and   proxybridge.com  okay enough to use?

I don't know these sites (and any good site at all because I don't usually use free proxies), but if they give you an IP address and port (something like "123.45.67.89:1080") for free and without registration - yes, they are good enough.

but make sure that you use SOCKS proxy, not HTTP proxy.

 

Note that free proxies are either slow or fall down very often because many people use these proxies simultaneously.  And not always for legitimate purposes, so when using free proxy you're very likely to run into "choose all pictures with traffic lights" much often than usual.

For stable connection with high speed I recommend finding a VPS/VDS in your particular state, order it with Linux OS and use it as a SOCKS proxy, no server configuration needed as SOCKS function is built-in in Linux. It will cost $3-10 for one month.