The short answer is yes, if you and your spouse both have self-employment income, each of you wold qualify for your own separate Solo 401(k). For more information on qualifications and contribution limits, see https://www.irs.gov/retirement-plans/one-participant-401k-plans.
As far as the follow-up questions regarding the different ways for your wife to show-self employment income without having to file a separate business tax return, (i.e., Form 1065), you could issue her a 1099-MISC for the value of the services she provides. You would both then file separate Schedule Cs reporting your income and expenses. Depending on whether or not your contractor work is performed under an incorporated business (i.e., an LLC) and whether or not you live in a community property state, you may be able to elect Qualified Joint Venture status. You would then both file separate Schedule Cs for your respective share of the business income and expenses without the need for filing a 1099.
For more information about Qualified Joint Ventures, including who can make that election and how to make that election, please see https://www.irs.gov/businesses/small-businesses-self-employed/election-for-married-couples-unincorpo... and Revenue Procedure 2002-69.
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