I built my core product myself as a solo founder and the product is live with a handful of paying customers, but I need to focus on product management and less on development. I know a couple of great coder possibilities, but I hate to give away equity that could potentially be worth a lot more than the cash in no time. What other alternatives are there?
You will always have to give people something they want (and you should give them even a little more than that as a gesture of being a good person), so you have to be imaginative and find the right people.
To do this, the most valuable assets you have are  your location,  how cool and fun of a person you are,  what you can offer in terms of connections / networking,  how cool your product is,  how cool the name / logo / website of your company is,  how good of a job title you can give,  'bonuses'.
The biggest pool of people to look into are high school or (less likely) college students, because they're relatively early in their career, and have the most to gain from what you can offer. The closer you are to scoring a 10 out of 10 in all of the things listed above, the easier it will be to find someone that's willing to work for you. You would be paying them in greatly enhancing their current life and future life prospects. Here's more details on the items in the list:
 If you're located somewhere cool (e.g. on the beach, in NY, SF, etc.), and could provide some kind of housing for free to someone from out of town (i.e. crash at your place or the office), that would be huge.
 If you're a fun and nice person and have fun friends who would make the work atmosphere a lot of fun, that will help hugely.
 If you're connected, or are obviously 'going places' that will help them with future job prospects, and just generally in connections with other cool projects. Even if you just went to a university that they want to go to for college or grad school, you could write a letter of rec for them.
[4 - 6] You need something that would be cool for them to put on their resume, and that will be impressive if people (e.g. parents, friends, future potential employers, etc.) look up the website. This will help them in future jobs, self confidence, etc.
 You should really give bonuses to show that you appreciate them and aren't completely just giving them stuff that you have 'lying around'. Give them money to buy lunch every day, or cook food for them yourself or something. Give them some stock, even if you multiply your stock by a million so it's essentially monetarily very little, giving them a couple thousand stock will still be giving them a part of something they helped with, so it's much bigger than it is monetarily. If you can think of other 'bonuses' like these, they'll help a _lot_ too.
As you move forward, if you want to discuss any other aspects of a lean early startup phase just send me a message,
best of luck!
Lee gave a good answer.
What we're talking about is sales and negotiation, and there is frequently something the customer values more than you do which can take the place of money or another asset in your exchange.
The truth is that hardly anyone suspects this is possible or ever asks.
Many joint ventures are structured this way: one side gives up something they have, but don't think is valuable, to the other, who does value it.
The key is in asking the questions to find out. Don't just throw random stuff at the prospect hoping something will stick. Ask. Get them to co-create the solution with you.