I see a lot of secured cards have an annual fee... and that to me isn't worth it...
Here are some links to No Annual Fee Secured Credit Cards
Most are Open to All... some credit unions may require hoops
Not sure if they all graduate or not... Does anyone want to chime in?
Secured Visa® Credit Card | First National Bank of Omaha
Also BOA if you apply for unsecured you may get countered with a 99/500 or No Annual Fee Secured Card
Thanks for making this list! 
- Discover graduates its secured cardholders at the 8-month statement.
"Starting eight months after you've been a secured credit card member, we'll review your account monthly to see if we can return your security deposit while you continue to enjoy your card benefits. These reviews will look for your responsible credit use across all your cards and loans, not just with Discover." — Discover Bank's FAQs section
- First National Bank of Omaha (FNBO) graduates its secured cardholders graduates at the 11-month statement.
"You may be able to get your deposit back automatically in as little as 11 months when you maintain a good payment history (subject to credit approval)." — First National Bank's secured card homepage
- Capital One graduates its secrued card holders at pretty much anytime. There are no solid data points from I can find, so I conclude that Capital One bases its descion to graduate on the consumer's credit report and the consumer's internal history with Capital One.
Finding: Capital One only advertises increasing the existing credit line based on credit worthiness and if the consumer sucessfully makes 5 on-time monthly payments. YMMV, of course. 
also didn't add PENFED Secured and PENFED Initiator (partial secured)
PenFed offers a Secured Visa card. The Rebuilder VISA credit card is for members
with poor credit history but who have regained control of their finances in the
last six months. 100% of the credit line will remain on hold in your share
account. The Rebuilder Visa secure card will have a 6-month expiration date.
Subsequent (renewal) cards will have a 12-month expiration date. After 12 months
of satisfactory repayment, you may apply for a regular VISA account. Please
note, approval for a secured VISA is not guaranteed. A loan application must be
submitted to consider your request and you must have $500.00 available in your
Regular Share account to start the application process. You may also apply for
the Initiator VISA credit card. The Initiator VISA credit card is similar to
Pentagon Federal's VISA Classic credit card product but is intended for those
members with limited or no credit experience. 50% of the credit line will remain
on hold in your share account. To qualify for this card, you cannot make more
than $2,000 a month.
with poor credit history but who have regained control of their finances in the
last six months. 100% of the credit line will remain on hold in your share
account. The Rebuilder Visa secure card will have a 6-month expiration date.
Subsequent (renewal) cards will have a 12-month expiration date. After 12 months
of satisfactory repayment, you may apply for a regular VISA account. Please
note, approval for a secured VISA is not guaranteed. A loan application must be
submitted to consider your request and you must have $500.00 available in your
Regular Share account to start the application process. You may also apply for
the Initiator VISA credit card. The Initiator VISA credit card is similar to
Pentagon Federal's VISA Classic credit card product but is intended for those
members with limited or no credit experience. 50% of the credit line will remain
on hold in your share account. To qualify for this card, you cannot make more
than $2,000 a month.
o apply for a secured credit card, please contact a Member Service
Representative at 1-800-247-5626, (541) 225-6700 or 510-376-7328 from a Class A
Military DSN phone line.
Representatives are available 7 days a week during the following hours:
Monday - Friday: 7:00 am to 11:00 pm ET
Saturday: 8:00 am to 11:00 pm ET
Sunday: 9:00 am to 5:30 pm ET
It would be nice if this could be a running thread to share data points etc.
In my case, I am looking for number 3 as I have NFCU and Discover. I can't try a few on the above list but a CU secured card might be my best option. Unfortunately SDFCU, Affinity and Unify all denied my memberships due to not being able to identify me. Each seems to be an almost certain approval for their secured cards if you can get in. Thankfully only SDFU was a hard inq.
I have Elements, Apple and DCU memberships but am not sure where to app.
Adding my data points:
NFCU nRewards approved 9-16 with a 480 EQ FICO 08
Discover Approved 10-18 with 546 EX FICO 08
3 collections, several 4.5 year old CO's
DCU offers a great secured product (doesn't graduate tho)... Elements is good too (i like the contactless)
Check this one out. A Cash Back Secured Card, 3-2-1 style with a smallish fee.
You must apply in branch apparently but could be a good one for those near a branch.
It has a high APR (24%) and a $29 fee but could be worth it if you pay in full and use it for dining (3%) and groceries (2%).
I wonder if it graduates to their standard no fee cash back card?
Another one for those in Carolina... Coastal Credit Union
No Fee, seems like you can not be denied. I joined a group last year to try and get in for this one but they denied my membership due to not living in NC.
Coastal CU Rate Advantage Secured Visa Credit Card
Here's a unique way to get your line of credit.
At Coastal, we care about the people in our community and we understand how important access to credit can be. That's why we offer the Rate Advantage Secured Visa Credit Card as a way to establish or rebuild your credit, regardless of your history. Other financial institutions may turn you down, but we care about our North Carolina members and always want to help you bank better. By keeping up your monthly payments, you can work toward a higher credit score and access to cards with lower rates and more benefits.
A potential card for those in the Pacific NW. Sadly you must live in Oregon or be in the insurance industry...
4.00% Fixed APR, No Fee and seemingly a low bar for approvals.
NW Preferred FCU Secured Visa Credit Card
"The good news is you don’t need great credit to obtain our secured Visa credit card. It’s perfect for rebuilding or establishing good credit."
To piggyback off of this, Allegacy FCU (another NC bank) also offers a secured card with no annual fee:
https://www.allegacy.org/cards-ways-to-pay/visa-platinum-secured/
Coastal FCU is in the Triangle area (and east) of NC, Allegacy is in the Triad area.
As an Allegacy member, I can attest to their fantastic customer service (unfortunately I didn't know FCUs had secured credit lines until too late ).